Focii of Ellipse

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.

Equation of the circle on the latusrectum of $y^2=8x$ as ends of diameter is

1. x²+y²-4y-12 =0

2. x²+y²+4x+12=0

3. x²+y²-4y+16=0

4. x²+y²-6x-12 =0

Q.

If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is

1. 4/5

2. 1/2

3. 2/3

4. 

Q.

A ray originating from the point (5, 0) is incident on the hyperbola $9x^2-16y^2=144$ at the point P with abscissa 8. Find the equation of the reflected ray after first reflection and point P lying in first quadrant.

1. $3\sqrt{3}x-13y-15\sqrt{3}=0$

2. $3\sqrt{3}x+13y+15\sqrt{3}=0$

3. 

4. $3\sqrt{3}x-13y+15\sqrt{3}=0$

Q.

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

1. tan θ

2. sin θ

3. cos θ

4. cotθ

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.

Let $F_1(x_1,0)$ and $F_2(x_2,0),$ where $x_1<0$ and $x_2>0$ be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1$ suppose a parabola having vertex at the origin and focus at $F_2$ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant.
The orthocentre of $\Delta F_{1}MN$ is

1. $(-\frac{9}{10},0)$

2. $(\frac{2}{3},0)$

3. $(\frac{9}{10},0)$

4. $(\frac{2}{3},\sqrt{6})$

Q. Rectangle $ABCD$ has area 200. An ellipse with area $200\pi$ passes through $A$ and $C$ and has foci at $B$ and $D$. If the perimeter of the rectangle is $P$, then the value of $\frac{P}{20}$ is

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. 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 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. $x^2+y^2-6y+5=0$