Transformation of Axes and Points
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Co-Ordinate system

88214 Find the transformed equation of \(x \cos \theta+y\) \(\sin \theta=p\), when the axes are rotated through an angle \(\theta\).

1 \(x=p\)
2 \(y=p\)
3 \(x+y=p\)
4 \(x-y=p\)
AP EAMCET-2020-17.09.2020
Co-Ordinate system

88215 When the origin is shifted to \((2,3)\) the transformed equation \(\mathbf{x}^{2}+3 x y-2 y^{2}+17 x-7 y-11=0\), then the original equation of curve is .......

1 \(x^{2}-2 y^{2}-3 x y+4 x-y+20=0\)
2 \(x^{2}-2 y^{2}+3 x y+4 x-y-20=0\)
3 \(x^{2}-2 y^{2}-3 x y-4 x-y+20=0\)
4 \(x^{2}-2 y^{2}-3 x y+4 x-y-20=0\)
AP EAMCET-2020-18.09.2020
Co-Ordinate system

88216 The polar equation of the line perpendicular to the line \(\sin \theta-\cos \theta=\frac{1}{\mathrm{r}}\) and passing through the point \(\left(2, \frac{\pi}{6}\right)\) is

1 \(\sin \theta+\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
2 \(\sin \theta-\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
3 \(\sin \theta+\cos \theta=\frac{\sqrt{3}-1}{\mathrm{r}}\)
4 \(\cos \theta-\sin \theta=\frac{\sqrt{3}}{\mathrm{r}}\)
AP EAMCET-2011
Co-Ordinate system

88217 The origin is translated to \((1,2)\). The point \((7\), 5) in the old system undergoes the following transformations successively.
I. Moves to the new point under the given translation of origin.
II. Translated through 2 units along the negative direction of the new \(\mathrm{X}\)-axis.
III. Rotated through an angle \(\frac{\pi}{4}\) about the origin of new system in the clockwise direction. The final position of the point \((7,5)\) is

1 \(\left(\frac{9}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
2 \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
3 \(\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
4 \(\left(\frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
AP EAMCET-2013
Co-Ordinate system

88218 If the point \(P(1,3)\) undergoes the following transformations successively.
(i) Reflection with respect to line \(y=x\)
(ii) Translation through 3 units along the positive direction of the \(\mathrm{X}\)-axis.
(iii) Rotation through and angles of \(\frac{\pi}{6}\) about the origin in the clockwise direction.
Then the final position of the point \(P\) is

1 \(\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)\)
2 \(\left(\frac{\sqrt{7}}{2}, \frac{5}{\sqrt{2}}\right)\)
3 \(\left(\frac{6+\sqrt{3}}{2}, \frac{1-6 \sqrt{3}}{2}\right)\)
4 \(\left(\frac{6+\sqrt{3}-1}{2}, \frac{6+\sqrt{3}}{2}\right)\)
AP EAMCET-2014
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Co-Ordinate system

88214 Find the transformed equation of \(x \cos \theta+y\) \(\sin \theta=p\), when the axes are rotated through an angle \(\theta\).

1 \(x=p\)
2 \(y=p\)
3 \(x+y=p\)
4 \(x-y=p\)
AP EAMCET-2020-17.09.2020
Co-Ordinate system

88215 When the origin is shifted to \((2,3)\) the transformed equation \(\mathbf{x}^{2}+3 x y-2 y^{2}+17 x-7 y-11=0\), then the original equation of curve is .......

1 \(x^{2}-2 y^{2}-3 x y+4 x-y+20=0\)
2 \(x^{2}-2 y^{2}+3 x y+4 x-y-20=0\)
3 \(x^{2}-2 y^{2}-3 x y-4 x-y+20=0\)
4 \(x^{2}-2 y^{2}-3 x y+4 x-y-20=0\)
AP EAMCET-2020-18.09.2020
Co-Ordinate system

88216 The polar equation of the line perpendicular to the line \(\sin \theta-\cos \theta=\frac{1}{\mathrm{r}}\) and passing through the point \(\left(2, \frac{\pi}{6}\right)\) is

1 \(\sin \theta+\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
2 \(\sin \theta-\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
3 \(\sin \theta+\cos \theta=\frac{\sqrt{3}-1}{\mathrm{r}}\)
4 \(\cos \theta-\sin \theta=\frac{\sqrt{3}}{\mathrm{r}}\)
AP EAMCET-2011
Co-Ordinate system

88217 The origin is translated to \((1,2)\). The point \((7\), 5) in the old system undergoes the following transformations successively.
I. Moves to the new point under the given translation of origin.
II. Translated through 2 units along the negative direction of the new \(\mathrm{X}\)-axis.
III. Rotated through an angle \(\frac{\pi}{4}\) about the origin of new system in the clockwise direction. The final position of the point \((7,5)\) is

1 \(\left(\frac{9}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
2 \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
3 \(\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
4 \(\left(\frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
AP EAMCET-2013
Co-Ordinate system

88218 If the point \(P(1,3)\) undergoes the following transformations successively.
(i) Reflection with respect to line \(y=x\)
(ii) Translation through 3 units along the positive direction of the \(\mathrm{X}\)-axis.
(iii) Rotation through and angles of \(\frac{\pi}{6}\) about the origin in the clockwise direction.
Then the final position of the point \(P\) is

1 \(\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)\)
2 \(\left(\frac{\sqrt{7}}{2}, \frac{5}{\sqrt{2}}\right)\)
3 \(\left(\frac{6+\sqrt{3}}{2}, \frac{1-6 \sqrt{3}}{2}\right)\)
4 \(\left(\frac{6+\sqrt{3}-1}{2}, \frac{6+\sqrt{3}}{2}\right)\)
AP EAMCET-2014
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Co-Ordinate system

88214 Find the transformed equation of \(x \cos \theta+y\) \(\sin \theta=p\), when the axes are rotated through an angle \(\theta\).

1 \(x=p\)
2 \(y=p\)
3 \(x+y=p\)
4 \(x-y=p\)
AP EAMCET-2020-17.09.2020
Co-Ordinate system

88215 When the origin is shifted to \((2,3)\) the transformed equation \(\mathbf{x}^{2}+3 x y-2 y^{2}+17 x-7 y-11=0\), then the original equation of curve is .......

1 \(x^{2}-2 y^{2}-3 x y+4 x-y+20=0\)
2 \(x^{2}-2 y^{2}+3 x y+4 x-y-20=0\)
3 \(x^{2}-2 y^{2}-3 x y-4 x-y+20=0\)
4 \(x^{2}-2 y^{2}-3 x y+4 x-y-20=0\)
AP EAMCET-2020-18.09.2020
Co-Ordinate system

88216 The polar equation of the line perpendicular to the line \(\sin \theta-\cos \theta=\frac{1}{\mathrm{r}}\) and passing through the point \(\left(2, \frac{\pi}{6}\right)\) is

1 \(\sin \theta+\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
2 \(\sin \theta-\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
3 \(\sin \theta+\cos \theta=\frac{\sqrt{3}-1}{\mathrm{r}}\)
4 \(\cos \theta-\sin \theta=\frac{\sqrt{3}}{\mathrm{r}}\)
AP EAMCET-2011
Co-Ordinate system

88217 The origin is translated to \((1,2)\). The point \((7\), 5) in the old system undergoes the following transformations successively.
I. Moves to the new point under the given translation of origin.
II. Translated through 2 units along the negative direction of the new \(\mathrm{X}\)-axis.
III. Rotated through an angle \(\frac{\pi}{4}\) about the origin of new system in the clockwise direction. The final position of the point \((7,5)\) is

1 \(\left(\frac{9}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
2 \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
3 \(\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
4 \(\left(\frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
AP EAMCET-2013
Co-Ordinate system

88218 If the point \(P(1,3)\) undergoes the following transformations successively.
(i) Reflection with respect to line \(y=x\)
(ii) Translation through 3 units along the positive direction of the \(\mathrm{X}\)-axis.
(iii) Rotation through and angles of \(\frac{\pi}{6}\) about the origin in the clockwise direction.
Then the final position of the point \(P\) is

1 \(\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)\)
2 \(\left(\frac{\sqrt{7}}{2}, \frac{5}{\sqrt{2}}\right)\)
3 \(\left(\frac{6+\sqrt{3}}{2}, \frac{1-6 \sqrt{3}}{2}\right)\)
4 \(\left(\frac{6+\sqrt{3}-1}{2}, \frac{6+\sqrt{3}}{2}\right)\)
AP EAMCET-2014
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Co-Ordinate system

88214 Find the transformed equation of \(x \cos \theta+y\) \(\sin \theta=p\), when the axes are rotated through an angle \(\theta\).

1 \(x=p\)
2 \(y=p\)
3 \(x+y=p\)
4 \(x-y=p\)
AP EAMCET-2020-17.09.2020
Co-Ordinate system

88215 When the origin is shifted to \((2,3)\) the transformed equation \(\mathbf{x}^{2}+3 x y-2 y^{2}+17 x-7 y-11=0\), then the original equation of curve is .......

1 \(x^{2}-2 y^{2}-3 x y+4 x-y+20=0\)
2 \(x^{2}-2 y^{2}+3 x y+4 x-y-20=0\)
3 \(x^{2}-2 y^{2}-3 x y-4 x-y+20=0\)
4 \(x^{2}-2 y^{2}-3 x y+4 x-y-20=0\)
AP EAMCET-2020-18.09.2020
Co-Ordinate system

88216 The polar equation of the line perpendicular to the line \(\sin \theta-\cos \theta=\frac{1}{\mathrm{r}}\) and passing through the point \(\left(2, \frac{\pi}{6}\right)\) is

1 \(\sin \theta+\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
2 \(\sin \theta-\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
3 \(\sin \theta+\cos \theta=\frac{\sqrt{3}-1}{\mathrm{r}}\)
4 \(\cos \theta-\sin \theta=\frac{\sqrt{3}}{\mathrm{r}}\)
AP EAMCET-2011
Co-Ordinate system

88217 The origin is translated to \((1,2)\). The point \((7\), 5) in the old system undergoes the following transformations successively.
I. Moves to the new point under the given translation of origin.
II. Translated through 2 units along the negative direction of the new \(\mathrm{X}\)-axis.
III. Rotated through an angle \(\frac{\pi}{4}\) about the origin of new system in the clockwise direction. The final position of the point \((7,5)\) is

1 \(\left(\frac{9}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
2 \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
3 \(\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
4 \(\left(\frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
AP EAMCET-2013
Co-Ordinate system

88218 If the point \(P(1,3)\) undergoes the following transformations successively.
(i) Reflection with respect to line \(y=x\)
(ii) Translation through 3 units along the positive direction of the \(\mathrm{X}\)-axis.
(iii) Rotation through and angles of \(\frac{\pi}{6}\) about the origin in the clockwise direction.
Then the final position of the point \(P\) is

1 \(\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)\)
2 \(\left(\frac{\sqrt{7}}{2}, \frac{5}{\sqrt{2}}\right)\)
3 \(\left(\frac{6+\sqrt{3}}{2}, \frac{1-6 \sqrt{3}}{2}\right)\)
4 \(\left(\frac{6+\sqrt{3}-1}{2}, \frac{6+\sqrt{3}}{2}\right)\)
AP EAMCET-2014
Join With Us for More Updates
Co-Ordinate system

88214 Find the transformed equation of \(x \cos \theta+y\) \(\sin \theta=p\), when the axes are rotated through an angle \(\theta\).

1 \(x=p\)
2 \(y=p\)
3 \(x+y=p\)
4 \(x-y=p\)
AP EAMCET-2020-17.09.2020
Co-Ordinate system

88215 When the origin is shifted to \((2,3)\) the transformed equation \(\mathbf{x}^{2}+3 x y-2 y^{2}+17 x-7 y-11=0\), then the original equation of curve is .......

1 \(x^{2}-2 y^{2}-3 x y+4 x-y+20=0\)
2 \(x^{2}-2 y^{2}+3 x y+4 x-y-20=0\)
3 \(x^{2}-2 y^{2}-3 x y-4 x-y+20=0\)
4 \(x^{2}-2 y^{2}-3 x y+4 x-y-20=0\)
AP EAMCET-2020-18.09.2020
Co-Ordinate system

88216 The polar equation of the line perpendicular to the line \(\sin \theta-\cos \theta=\frac{1}{\mathrm{r}}\) and passing through the point \(\left(2, \frac{\pi}{6}\right)\) is

1 \(\sin \theta+\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
2 \(\sin \theta-\cos \theta=\frac{\sqrt{3}+1}{\mathrm{r}}\)
3 \(\sin \theta+\cos \theta=\frac{\sqrt{3}-1}{\mathrm{r}}\)
4 \(\cos \theta-\sin \theta=\frac{\sqrt{3}}{\mathrm{r}}\)
AP EAMCET-2011
Co-Ordinate system

88217 The origin is translated to \((1,2)\). The point \((7\), 5) in the old system undergoes the following transformations successively.
I. Moves to the new point under the given translation of origin.
II. Translated through 2 units along the negative direction of the new \(\mathrm{X}\)-axis.
III. Rotated through an angle \(\frac{\pi}{4}\) about the origin of new system in the clockwise direction. The final position of the point \((7,5)\) is

1 \(\left(\frac{9}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
2 \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
3 \(\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
4 \(\left(\frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
AP EAMCET-2013
Co-Ordinate system

88218 If the point \(P(1,3)\) undergoes the following transformations successively.
(i) Reflection with respect to line \(y=x\)
(ii) Translation through 3 units along the positive direction of the \(\mathrm{X}\)-axis.
(iii) Rotation through and angles of \(\frac{\pi}{6}\) about the origin in the clockwise direction.
Then the final position of the point \(P\) is

1 \(\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)\)
2 \(\left(\frac{\sqrt{7}}{2}, \frac{5}{\sqrt{2}}\right)\)
3 \(\left(\frac{6+\sqrt{3}}{2}, \frac{1-6 \sqrt{3}}{2}\right)\)
4 \(\left(\frac{6+\sqrt{3}-1}{2}, \frac{6+\sqrt{3}}{2}\right)\)
AP EAMCET-2014