Chord of Contact - Practice Questions & MCQ

Let the tangent to the circle $\mathrm{C}_1: x^2+y^2=2$ at the point $\mathrm{M}(-1,1)$ intersect the circle $\mathrm{C}_2:(x-3)^2+(y-2)^2=5$, at two distinct points $A$ and $B$. If the tangents to $C_2$ at the points $A$ and $B$ intersect at $N$, then the area of the triangle ANB is equal to :

Let the tangents at two points A and B on the circle $\mathrm{x}^2+\mathrm{y}^2-4 \mathrm{x}+3=0$ meet at origin $\mathrm{O}(0,0)$. Then the area of the triangle OAB is:

The equation of the chord of contact of the origin w.r.t. circle  is
 

Equation of chord  of circle passing through  such that , is given by:

If chord of contacts are drawn to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ from different points on the line $4 x+25 y=100$, then each of these chords pass through which point

The chords of contact of the pair of tangents drawn from each point on the line $2 \mathrm{x}+\mathrm{y}=4$ to the circle $\mathrm{x}^2+\mathrm{y}^2=1$ pass through a fixed point -

The equation of chord of contact of point $(2,-1)$ with respect to parabola $y=x^2-2 x+2$ is

The locus of midpoints of the chords of the circle $x^2+y^2=4$ that pass through the point $(1,1)$ is

Equation of chord AB of circle $\mathrm{x}^2+\mathrm{y}^2=2$ passing through $\mathrm{P}(2,2)$ such that $\frac{\mathrm{PB} }{ \mathrm{PA}}=3$ , is given by-

The point of intersection of tangents to $\frac{x^2}{16}+\frac{y^2}{9}=1$ at points where the line $x+8 y-8=0$ intersects it, is