Focii of Ellipse

Q.

If $P$ be the point $\left(1,0\right)$ and $Q$ a point on the locus of $y^2=8x$. The locus of mid-point of $PQ$ is

1. $x^2–4y+2=0$

2. $x^2+4y+2=0$

3. $y^2–4x+2=0$

4. $y^2+4x-2=0$

Q. The coordinates of the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ is/are

1. $(\sqrt{5},0)$
2. $(2\sqrt{5},0)$
3. $(-\sqrt{5},0)$
4. $(-2\sqrt{5},0)$

Q. The perimeter of a triangle is 20 and the points (-2, -3) and (-2, 3) are two of the vertices of it. Then the locus of third vertex is :

1. $\frac{(x-2{)}^2}{49}+\frac{y^2}{40}=1$
2. $\frac{(x+2{)}^2}{49}+\frac{y^2}{40}=1$
3. $\frac{(x+2{)}^2}{40}+\frac{y^2}{49}=1$
4. $\frac{(x-2{)}^2}{40}+\frac{y^2}{49}=1$

Q. A man running round a race course notes that the sum of the distances of two flag posts from him is 8 meters.The area of the path he encloses in square meters if the distance between flag posts is 4 is

1. $15\sqrt{3}\pi$
2. $12\sqrt{3}\pi$
3. $18\sqrt{3}\pi$
4. $8\sqrt{3}\pi$

Q.

let $S$, $S^1$ be the foci of an ellipse. If $\angle BS{S}^1$ = $\theta$, where B is any point on the ellipse. Then its eccentricity is

1. tan $\theta$

2. sin $\theta$

3. cos $\theta$

4. cot $\theta$

Q. If $(3,4)$ and $(8,6)$ are the foci of an ellipse passing through the origin, then the eccentricity of the ellipse is

1. $\frac{\sqrt{29}}{15}$
2. $\frac{1}{2}$
3. $\frac{1}{\sqrt{2}}$
4. $\sqrt{\frac{15}{29}}$

Q.

The distance between the foci of the ellipse x=5cos$\theta$, y=4sin$\theta$ is

1. 8

2. 10

3. 7

4. 6

Q. The equation of the ellipse having its centre at the point $(2,-3)$, one focus at $(3,-3)$ and one vertex at $(4,-3)$ is

1. $\frac{(x+3{)}^2}{4}+\frac{(y-2{)}^2}{3}=1$
2. $\frac{(x+3{)}^2}{3}+\frac{(y-2{)}^2}{4}=1$
3. $\frac{(x-2{)}^2}{3}+\frac{(y+3{)}^2}{4}=1$
4. $\frac{(x-2{)}^2}{4}+\frac{(y+3{)}^2}{3}=1$

Q. The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having centre at $(0,3)$ is

1. $x^2+y^2-6y-7=0$
2. $x^2+y^2-6y+7=0$
3. $x^2+y^2-6y-5=0$
4. $x^2+y^2-6y+5=0$

Q. The coordinates of the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{16}=1$ is/are

1. $(\sqrt{5},0)$
2. $(2\sqrt{5},0)$
3. $(-\sqrt{5},0)$
4. $(-2\sqrt{5},0)$