EllipseHardBloom L2
Question
If ellipses $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ be described having the same major axis, but a variable minor axis, then for all values of $b$, the tangents at the ends of their latus rectum can pass through :
Options
A.$(0,a)$
B.$(0, - a)$
C.$(0,2a)$
D.$(0, - 2a)$
Solution
Sol. 
Tangents at extremities of L.R. are
$$\frac{xe}{a} + \frac{y}{a} = 1$$
or $\ \frac{xe}{a} - \frac{y}{a} = 1$
$$\begin{matrix} & xe + (y - a) = 0 \\ & xe - (y + a) = 0 \\ & \text{~}\text{Fixed points are}\text{~}(0,a)\ \text{~}\text{or}\text{~}(0, - a) \end{matrix}$$
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