Chord of Contact: Ellipse

Q.

What is the equation of chord of contact of tangents drawn from P(10, 8) to the ellipse
$\frac{x^2}{25}+\frac{y^2}{16}=1$.

1. $4x+5y=10$

2. $5x-4y=10$

3. $4x-5y=5$

4. $4x-5y=10$

Q. If tangent to parabola $y^2=4ax$ intersects ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at $A$ and $B,$ then the locus of point of intersection of tangents at $A$ and $B,$ is

1. straight line
2. parabola with length of latus rectum $\frac{b^4}{a^3}$ unit
3. ellipse
4. parabola with length of latus rectum $\frac{a^4}{b^3}$ unit

Q.

What is the slope of a chord centered at (3, 2) in the circle $x^2+y^2=25$

1. -1/2

2. 1/2

3. -3/2

4. 3/2

Q. Find the equation of chord of contact of tangents drawn from a point $(5,5)$ to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$

1. None of the above
2. $\frac{x}{9}+\frac{y}{4}=1$
3. $\frac{x}{9}+\frac{y}{4}=4$
4. $\frac{x}{9}+\frac{y}{4}=\frac{1}{5}$

Q.

What is the equation of chord of contact of tangents drawn from P(10, 8) to the ellipse
$\frac{x^2}{25}+\frac{y^2}{16}=1$.

1. $4x+5y=10$

2. $5x-4y=10$

3. $4x-5y=5$

4. $4x-5y=10$

Q.

Which of the following gives the equation of director circle of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$?

1. $x^2-y^2=9$

2. $x^2+y^2=41$

3. $x^2+y^2=9$

4. $x^2+y^2=25$

Q. If the chord through the points whose eccentric angles are $\theta$ and $\varphi$ on the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ passes through a focus, then the value of $\tan \left(\frac{\theta }{2}\right)\tan \left(\frac{\varphi }{2}\right)$is

1. $\frac{1}{9}$
2. $-9$
3. $-\frac{1}{9}$
4. $9$