A) \[a+b\]
B) \[{{a}^{2}}+{{b}^{2}}\]
C) \[{{a}^{2}}\]
D) \[{{b}^{2}}\]
Correct Answer: D
Solution :
Let \[P(a\cos \theta ,\,\,b\sin \theta )\] be any point on the ellipse. Then, equation of the tangent at \[P\] is \[\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1\] It cuts the lines\[x=a\]and\[x=-a\] \[L\left( a,\,\,\frac{b(1-\cos \theta )}{\sin \theta } \right)\]and\[L'\left( -a,\,\,\frac{b(1+\cos \theta )}{\sin \theta } \right)\]respectively. Since, \[A\] and \[A'\] are the vertices of given ellipse. Therefore, coordinates \[A(a,\,\,0)\] and\[B(0,\,\,-a)\]. \[\therefore \] \[AL=\frac{b(1-\cos \theta )}{\sin \theta }\]and\[AL'=\frac{b(1+\cos \theta )}{\sin \theta }\]You need to login to perform this action.
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