EllipseHardBloom L2
Question
Ellipses are described with line segment $AB$ as the fixed major axis. The locus of an end of a latus rectum is:
Options
A.straight line
B.parabola
C.circle
D.ellipse
Solution
Sol.(b)
$$\begin{matrix} h & \ = ae \\ k & \ = \frac{b^{2}}{a} = a\left( 1 - e^{2} \right) = a\left( 1 - \frac{h^{2}}{a^{2}} \right) \\ & \ \\ ay & \ = \left( a^{2} - x^{2} \right) \\ x^{2} & \ = a(a - y) \rightarrow \text{~}\text{Parabola}\text{~} \\ & \\ & \\ & \end{matrix}$$
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