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Parabola

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By Expert Faculty of Sri Chaitanya
Question

The  length of the latus rectum of the parabola 289(x3)2+(y1)2=(15x8y+13)2  is equal to

Moderate
Solution

We can write the given equation  as

(x3)2+(y1)2=|15x8y+13|17

This represents a parabola with focus at (3, 1) and directrix as 15x-8y+ 13 =0.

L= length of latus rectum

=2[distance of focus from the directrix]

=2|15(3)8(1)+13|17=100175.88


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