A set of lines $x+y-2 +A(2x+y-3)=0$ represent incident rays on an ellipse $s = 0$ and $2x+3y-23+B(2x+y-3)=0$ represents the set of reflective rays from the ellipse where $A,B \in \Bbb R$.
If $p( 3, 7 )$ is a point on the ellipse normal at which meets the major Axis at $N$, find eccentricity of the ellipse.
I am unable to even proceed please give small help
The first set of lines are all passing through $(1,1)$ while the second set passes through $\left(-\dfrac{7}{2}, 10\right)$. By the Reflective Property of Ellipse
we can see that the above points are the two focii, $S,S'$ of the ellipse.
To find length of major axis use $2a= SP+S'P$ with $P(3,7)$. Then use that $SS'=2ae$ where $e$ is the required eccentricity.