Transformation of Axes and Points
Co-Ordinate system

88202 The angle between the lines whose intercepts on the axis are \(a,-b\) and \(b,-a\) respectively, is

1 \(\tan ^{-1} \frac{a^{2}-b^{2}}{a b}\)
2 \(\tan ^{-1} \frac{\mathrm{b}^{2}-\mathrm{a}^{2}}{2}\)
3 \(\tan ^{-1} \frac{b^{2}-a^{2}}{2 a b}\)
4 None of these
Co-Ordinate system

88201 If \(P_{1}\) and \(P_{2}\) be the length of perpendiculars from the origin upon the straight lines \(x \sec \theta+y \operatorname{cosec} \theta=a\) and
\(x \cos \theta-y \sin \theta=a \cos 2 \theta\) respectively, then the value of \(4 \mathrm{P}_{1}{ }^{2}+\mathrm{P}_{2}{ }^{2}\).

1 \(a^{2}\)
2 \(2 \mathrm{a}^{2}\)
3 \(a^{2} / 2\)
4 \(3 \mathrm{a}^{2}\)
Co-Ordinate system

88203 A ray of light coming from the point \((1,2)\) is reflected at a point \(A\) on the \(x\)-axis and then passes through the point \((5,3)\). The coordinates of the point \(A\) is

1 \(\left(\frac{13}{5}, 0\right)\)
2 \(\left(\frac{5}{13}, 0\right)\)
3 \((-7,0)\)
4 None of these
Co-Ordinate system

88204 The equation of the line with gradient \(-3 / 2\), which is concurrent with the lines \(4 x+3 y-7=0\) and \(8 x+5 y-1=0\), is

1 \(3 x+2 y-2=0\)
2 \(3 x+2 y-63=0\)
3 \(2 y-3 x-2=0\)
4 \(2 y-3 x-63=0\)
Co-Ordinate system

88205 Equation of line passing through the point (1, 2) and perpendicular to the line \(y=3 x-1\) is

1 \(x-3 y=0\)
2 \(x+3 y=0\)
3 \(x+3 y-7=0\)
4 \(x+3 y+7=0\)
Co-Ordinate system

88202 The angle between the lines whose intercepts on the axis are \(a,-b\) and \(b,-a\) respectively, is

1 \(\tan ^{-1} \frac{a^{2}-b^{2}}{a b}\)
2 \(\tan ^{-1} \frac{\mathrm{b}^{2}-\mathrm{a}^{2}}{2}\)
3 \(\tan ^{-1} \frac{b^{2}-a^{2}}{2 a b}\)
4 None of these
Co-Ordinate system

88201 If \(P_{1}\) and \(P_{2}\) be the length of perpendiculars from the origin upon the straight lines \(x \sec \theta+y \operatorname{cosec} \theta=a\) and
\(x \cos \theta-y \sin \theta=a \cos 2 \theta\) respectively, then the value of \(4 \mathrm{P}_{1}{ }^{2}+\mathrm{P}_{2}{ }^{2}\).

1 \(a^{2}\)
2 \(2 \mathrm{a}^{2}\)
3 \(a^{2} / 2\)
4 \(3 \mathrm{a}^{2}\)
Co-Ordinate system

88203 A ray of light coming from the point \((1,2)\) is reflected at a point \(A\) on the \(x\)-axis and then passes through the point \((5,3)\). The coordinates of the point \(A\) is

1 \(\left(\frac{13}{5}, 0\right)\)
2 \(\left(\frac{5}{13}, 0\right)\)
3 \((-7,0)\)
4 None of these
Co-Ordinate system

88204 The equation of the line with gradient \(-3 / 2\), which is concurrent with the lines \(4 x+3 y-7=0\) and \(8 x+5 y-1=0\), is

1 \(3 x+2 y-2=0\)
2 \(3 x+2 y-63=0\)
3 \(2 y-3 x-2=0\)
4 \(2 y-3 x-63=0\)
Co-Ordinate system

88205 Equation of line passing through the point (1, 2) and perpendicular to the line \(y=3 x-1\) is

1 \(x-3 y=0\)
2 \(x+3 y=0\)
3 \(x+3 y-7=0\)
4 \(x+3 y+7=0\)
Co-Ordinate system

88202 The angle between the lines whose intercepts on the axis are \(a,-b\) and \(b,-a\) respectively, is

1 \(\tan ^{-1} \frac{a^{2}-b^{2}}{a b}\)
2 \(\tan ^{-1} \frac{\mathrm{b}^{2}-\mathrm{a}^{2}}{2}\)
3 \(\tan ^{-1} \frac{b^{2}-a^{2}}{2 a b}\)
4 None of these
Co-Ordinate system

88201 If \(P_{1}\) and \(P_{2}\) be the length of perpendiculars from the origin upon the straight lines \(x \sec \theta+y \operatorname{cosec} \theta=a\) and
\(x \cos \theta-y \sin \theta=a \cos 2 \theta\) respectively, then the value of \(4 \mathrm{P}_{1}{ }^{2}+\mathrm{P}_{2}{ }^{2}\).

1 \(a^{2}\)
2 \(2 \mathrm{a}^{2}\)
3 \(a^{2} / 2\)
4 \(3 \mathrm{a}^{2}\)
Co-Ordinate system

88203 A ray of light coming from the point \((1,2)\) is reflected at a point \(A\) on the \(x\)-axis and then passes through the point \((5,3)\). The coordinates of the point \(A\) is

1 \(\left(\frac{13}{5}, 0\right)\)
2 \(\left(\frac{5}{13}, 0\right)\)
3 \((-7,0)\)
4 None of these
Co-Ordinate system

88204 The equation of the line with gradient \(-3 / 2\), which is concurrent with the lines \(4 x+3 y-7=0\) and \(8 x+5 y-1=0\), is

1 \(3 x+2 y-2=0\)
2 \(3 x+2 y-63=0\)
3 \(2 y-3 x-2=0\)
4 \(2 y-3 x-63=0\)
Co-Ordinate system

88205 Equation of line passing through the point (1, 2) and perpendicular to the line \(y=3 x-1\) is

1 \(x-3 y=0\)
2 \(x+3 y=0\)
3 \(x+3 y-7=0\)
4 \(x+3 y+7=0\)
Co-Ordinate system

88202 The angle between the lines whose intercepts on the axis are \(a,-b\) and \(b,-a\) respectively, is

1 \(\tan ^{-1} \frac{a^{2}-b^{2}}{a b}\)
2 \(\tan ^{-1} \frac{\mathrm{b}^{2}-\mathrm{a}^{2}}{2}\)
3 \(\tan ^{-1} \frac{b^{2}-a^{2}}{2 a b}\)
4 None of these
Co-Ordinate system

88201 If \(P_{1}\) and \(P_{2}\) be the length of perpendiculars from the origin upon the straight lines \(x \sec \theta+y \operatorname{cosec} \theta=a\) and
\(x \cos \theta-y \sin \theta=a \cos 2 \theta\) respectively, then the value of \(4 \mathrm{P}_{1}{ }^{2}+\mathrm{P}_{2}{ }^{2}\).

1 \(a^{2}\)
2 \(2 \mathrm{a}^{2}\)
3 \(a^{2} / 2\)
4 \(3 \mathrm{a}^{2}\)
Co-Ordinate system

88203 A ray of light coming from the point \((1,2)\) is reflected at a point \(A\) on the \(x\)-axis and then passes through the point \((5,3)\). The coordinates of the point \(A\) is

1 \(\left(\frac{13}{5}, 0\right)\)
2 \(\left(\frac{5}{13}, 0\right)\)
3 \((-7,0)\)
4 None of these
Co-Ordinate system

88204 The equation of the line with gradient \(-3 / 2\), which is concurrent with the lines \(4 x+3 y-7=0\) and \(8 x+5 y-1=0\), is

1 \(3 x+2 y-2=0\)
2 \(3 x+2 y-63=0\)
3 \(2 y-3 x-2=0\)
4 \(2 y-3 x-63=0\)
Co-Ordinate system

88205 Equation of line passing through the point (1, 2) and perpendicular to the line \(y=3 x-1\) is

1 \(x-3 y=0\)
2 \(x+3 y=0\)
3 \(x+3 y-7=0\)
4 \(x+3 y+7=0\)
Co-Ordinate system

88202 The angle between the lines whose intercepts on the axis are \(a,-b\) and \(b,-a\) respectively, is

1 \(\tan ^{-1} \frac{a^{2}-b^{2}}{a b}\)
2 \(\tan ^{-1} \frac{\mathrm{b}^{2}-\mathrm{a}^{2}}{2}\)
3 \(\tan ^{-1} \frac{b^{2}-a^{2}}{2 a b}\)
4 None of these
Co-Ordinate system

88201 If \(P_{1}\) and \(P_{2}\) be the length of perpendiculars from the origin upon the straight lines \(x \sec \theta+y \operatorname{cosec} \theta=a\) and
\(x \cos \theta-y \sin \theta=a \cos 2 \theta\) respectively, then the value of \(4 \mathrm{P}_{1}{ }^{2}+\mathrm{P}_{2}{ }^{2}\).

1 \(a^{2}\)
2 \(2 \mathrm{a}^{2}\)
3 \(a^{2} / 2\)
4 \(3 \mathrm{a}^{2}\)
Co-Ordinate system

88203 A ray of light coming from the point \((1,2)\) is reflected at a point \(A\) on the \(x\)-axis and then passes through the point \((5,3)\). The coordinates of the point \(A\) is

1 \(\left(\frac{13}{5}, 0\right)\)
2 \(\left(\frac{5}{13}, 0\right)\)
3 \((-7,0)\)
4 None of these
Co-Ordinate system

88204 The equation of the line with gradient \(-3 / 2\), which is concurrent with the lines \(4 x+3 y-7=0\) and \(8 x+5 y-1=0\), is

1 \(3 x+2 y-2=0\)
2 \(3 x+2 y-63=0\)
3 \(2 y-3 x-2=0\)
4 \(2 y-3 x-63=0\)
Co-Ordinate system

88205 Equation of line passing through the point (1, 2) and perpendicular to the line \(y=3 x-1\) is

1 \(x-3 y=0\)
2 \(x+3 y=0\)
3 \(x+3 y-7=0\)
4 \(x+3 y+7=0\)