Equation of Pair of Tangents: Ellipse

Q.

Find the locus of point of intersection of perpendicular tangents to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$

1. x² + y² = 16

2. x² + y² = 7

3. x² + y² = 23

4. x² + y² = 9

Q.

Find the equation of pair of tangents to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ from (5, 4)

1. 4x + 5y - xy = 20

2. 4x + 5y - xy = 21

3. 4x + 5y + xy = 40

4. 5x + 4y + xy = 61

Q.

Focal chord to $y^2=16xistangentto(x-6{)}^2+y^2=2$ then the possible values of the slopes of this chord(s), are

1. 

2. 

3. 

4. 

Q. An ellipse whose major axis is parallel to $x-$axis is such that the segments of a focal chord are of $1$ and $3$ units. The lines $ax+by+c=0$ are the chords of the ellipse such that $a,b,c$ are in A.P. and bisected by the point at which they are concurrent. The equation of auxiliary circle is $x^2+y^2+2\alpha x+2\beta y-2\alpha -1=0.$ Then

1. The locus of perpendicular tangents to the ellipse is $(x-1{)}^2+(y+2{)}^2=7$
2. The locus of perpendicular tangents to the ellipse is $(x-1{)}^2+(y+2{)}^2=19$
3. Area of auxiliary circle is $2\pi$ sq. unit
4. Eccentricity of the ellipse is $\frac{1}{2}$

Q. Tangents are drawn through the point $(4,\sqrt{3})$ to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1.$ The points at which these tangents touch the ellipse are

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