Standard and General Form of Equation of a Circle
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Conic Section

119680 The diameter of \(16 x^2-9 y^2=144\) which
conjugate to \(x=2 y\) is

1 \(y=\frac{32 x}{9}\)
2 \(x=\frac{16}{9} y\)
3 \(y=\frac{16}{9} x\)
4 None of these
Manipal UGET-201
Conic Section

119690 The polar equation of the circle with centre at \(\left(2, \frac{\pi}{2}\right)\) and radius 3 units is

1 \(\mathrm{r}^2+4 \mathrm{r} \cos \theta=5\)
2 \(\mathrm{r}^2+4 \mathrm{r} \sin \theta=5\)
3 \(\mathrm{r}^2-4 \mathrm{r} \sin \theta=5\)
4 \(\mathrm{r}^2-4 \mathrm{r} \cos \theta=5\)
Assam CEE-2022
Conic Section

119681 The equation of the circle which passes throug the points \((2,3)\) and \((4,5)\) and the centre lies 0 the straight line \(y-4 x+3=0\) is

1 \(x^2+y^2+4 x-10 y+25=0\)
2 \(x^2+y^2-4 x-10 y+16=0\)
3 \(x^2+y^2-4 x-10 y+25=0\)
4 None of the above
Manipal UGET-201
Conic Section

119682 The point \((-15,21)\) lies
#[Qdiff: Hard, QCat: Numerical Based, examname: is, By comparing equation (i) with standard equation, \(x^2+y^2=r^2\), \(r^2=625\), \(r=25\), Distance of the point from the centre is, \(d=\sqrt{\left(0-(-15)^2+(0-21)^2\right.}\), \(=\sqrt{225+441}=25.61>25\)Thus the point \((-15,21)\) lies out-side of circle, 65. Let \(\mathbf{C}\) be the circle with centre \((0,0)\) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle \(C\) that subtend an angle of \(\frac{2 \pi}{3}\) at its centre,

1 Outside the circle \(x^2+y^2=729\)
2 Outside the circle \(x^2+y^2=625\)
3 Inside the circle \(x^2+y^2=529\)
4 Inside the circle \(x^2+y^2=576\)
is
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Conic Section

119680 The diameter of \(16 x^2-9 y^2=144\) which
conjugate to \(x=2 y\) is

1 \(y=\frac{32 x}{9}\)
2 \(x=\frac{16}{9} y\)
3 \(y=\frac{16}{9} x\)
4 None of these
Manipal UGET-201
Conic Section

119690 The polar equation of the circle with centre at \(\left(2, \frac{\pi}{2}\right)\) and radius 3 units is

1 \(\mathrm{r}^2+4 \mathrm{r} \cos \theta=5\)
2 \(\mathrm{r}^2+4 \mathrm{r} \sin \theta=5\)
3 \(\mathrm{r}^2-4 \mathrm{r} \sin \theta=5\)
4 \(\mathrm{r}^2-4 \mathrm{r} \cos \theta=5\)
Assam CEE-2022
Conic Section

119681 The equation of the circle which passes throug the points \((2,3)\) and \((4,5)\) and the centre lies 0 the straight line \(y-4 x+3=0\) is

1 \(x^2+y^2+4 x-10 y+25=0\)
2 \(x^2+y^2-4 x-10 y+16=0\)
3 \(x^2+y^2-4 x-10 y+25=0\)
4 None of the above
Manipal UGET-201
Conic Section

119682 The point \((-15,21)\) lies
#[Qdiff: Hard, QCat: Numerical Based, examname: is, By comparing equation (i) with standard equation, \(x^2+y^2=r^2\), \(r^2=625\), \(r=25\), Distance of the point from the centre is, \(d=\sqrt{\left(0-(-15)^2+(0-21)^2\right.}\), \(=\sqrt{225+441}=25.61>25\)Thus the point \((-15,21)\) lies out-side of circle, 65. Let \(\mathbf{C}\) be the circle with centre \((0,0)\) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle \(C\) that subtend an angle of \(\frac{2 \pi}{3}\) at its centre,

1 Outside the circle \(x^2+y^2=729\)
2 Outside the circle \(x^2+y^2=625\)
3 Inside the circle \(x^2+y^2=529\)
4 Inside the circle \(x^2+y^2=576\)
is
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Conic Section

119680 The diameter of \(16 x^2-9 y^2=144\) which
conjugate to \(x=2 y\) is

1 \(y=\frac{32 x}{9}\)
2 \(x=\frac{16}{9} y\)
3 \(y=\frac{16}{9} x\)
4 None of these
Manipal UGET-201
Conic Section

119690 The polar equation of the circle with centre at \(\left(2, \frac{\pi}{2}\right)\) and radius 3 units is

1 \(\mathrm{r}^2+4 \mathrm{r} \cos \theta=5\)
2 \(\mathrm{r}^2+4 \mathrm{r} \sin \theta=5\)
3 \(\mathrm{r}^2-4 \mathrm{r} \sin \theta=5\)
4 \(\mathrm{r}^2-4 \mathrm{r} \cos \theta=5\)
Assam CEE-2022
Conic Section

119681 The equation of the circle which passes throug the points \((2,3)\) and \((4,5)\) and the centre lies 0 the straight line \(y-4 x+3=0\) is

1 \(x^2+y^2+4 x-10 y+25=0\)
2 \(x^2+y^2-4 x-10 y+16=0\)
3 \(x^2+y^2-4 x-10 y+25=0\)
4 None of the above
Manipal UGET-201
Conic Section

119682 The point \((-15,21)\) lies
#[Qdiff: Hard, QCat: Numerical Based, examname: is, By comparing equation (i) with standard equation, \(x^2+y^2=r^2\), \(r^2=625\), \(r=25\), Distance of the point from the centre is, \(d=\sqrt{\left(0-(-15)^2+(0-21)^2\right.}\), \(=\sqrt{225+441}=25.61>25\)Thus the point \((-15,21)\) lies out-side of circle, 65. Let \(\mathbf{C}\) be the circle with centre \((0,0)\) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle \(C\) that subtend an angle of \(\frac{2 \pi}{3}\) at its centre,

1 Outside the circle \(x^2+y^2=729\)
2 Outside the circle \(x^2+y^2=625\)
3 Inside the circle \(x^2+y^2=529\)
4 Inside the circle \(x^2+y^2=576\)
is
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Conic Section

119680 The diameter of \(16 x^2-9 y^2=144\) which
conjugate to \(x=2 y\) is

1 \(y=\frac{32 x}{9}\)
2 \(x=\frac{16}{9} y\)
3 \(y=\frac{16}{9} x\)
4 None of these
Manipal UGET-201
Conic Section

119690 The polar equation of the circle with centre at \(\left(2, \frac{\pi}{2}\right)\) and radius 3 units is

1 \(\mathrm{r}^2+4 \mathrm{r} \cos \theta=5\)
2 \(\mathrm{r}^2+4 \mathrm{r} \sin \theta=5\)
3 \(\mathrm{r}^2-4 \mathrm{r} \sin \theta=5\)
4 \(\mathrm{r}^2-4 \mathrm{r} \cos \theta=5\)
Assam CEE-2022
Conic Section

119681 The equation of the circle which passes throug the points \((2,3)\) and \((4,5)\) and the centre lies 0 the straight line \(y-4 x+3=0\) is

1 \(x^2+y^2+4 x-10 y+25=0\)
2 \(x^2+y^2-4 x-10 y+16=0\)
3 \(x^2+y^2-4 x-10 y+25=0\)
4 None of the above
Manipal UGET-201
Conic Section

119682 The point \((-15,21)\) lies
#[Qdiff: Hard, QCat: Numerical Based, examname: is, By comparing equation (i) with standard equation, \(x^2+y^2=r^2\), \(r^2=625\), \(r=25\), Distance of the point from the centre is, \(d=\sqrt{\left(0-(-15)^2+(0-21)^2\right.}\), \(=\sqrt{225+441}=25.61>25\)Thus the point \((-15,21)\) lies out-side of circle, 65. Let \(\mathbf{C}\) be the circle with centre \((0,0)\) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle \(C\) that subtend an angle of \(\frac{2 \pi}{3}\) at its centre,

1 Outside the circle \(x^2+y^2=729\)
2 Outside the circle \(x^2+y^2=625\)
3 Inside the circle \(x^2+y^2=529\)
4 Inside the circle \(x^2+y^2=576\)
is
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