Q.
Line $L =0$ cuts the conic $S =0$ at $A$ and $B$ and the equation $S +\lambda L ^2=0$ represent a circle for some $\lambda=\lambda_1$ (say), the circle $S+\lambda_1 L^2=0$ will touch the conic $S=0$ at both $A$ and $B$. Also if $L=0$ is tangent to conic $S=0$ the circle $S+\lambda_1 L^2=0$ has radius equal to radius of curvature of the conic at the point of contact.
Radius of curvature at the end point of major axis of ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is equal to -
Conic Sections
Solution: