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With a given point and line as focus and...

With a given point and line as focus and directrix, a series of ellipses are described. The locus of the extremities of their minor axis is an ellipse (b) a parabola a hyperbola (d) none of these

A

an ellipse

B

a parabola

C

a hyperbola

D

none of these

Text Solution

Verified by Experts

Let S be the given focus and ZM be the given directrix. Then,
`SZ=(a)/(e)-ae`
`=(a)/(e)(1-e^(2))`
`=(b^(2))/(ae)k` (say)

Now, take SC as the x-axis and LS'L as the y-axis . Let (x,y() be the coordinaters of B with respect to these axes. Then , x=SC=ae and y =CB=b b. Hence,
`(x^(2))/(a^(2))=(b^(2))/(ae)=SZ`
Which is constan.
Therefore, `y^(2)=kx` is the required locus which is a parabola.
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