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Question

The length of the latus-rectum of the parabola 169{(x−1)2+(y−3)2}=(5x−12y+17)2 is

A
1213
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B
1413
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C
2813
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D
3113
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Solution

The correct option is C 2813
The given equation can be written as (x1)2+(y3)2=(5x12y+1713)2
This is of the form PS = PM, where P is the point (x,y) on the parabola, PM is the perpendicular distance of P from the line 5x-12y+17 = 0(directrix) and PS is the of P from focus (1,3)
So we get focus = (1,3) and directrix equal to 5x-12y+17 = 0.
Length of latus rectum =4a
Perpendicular distance from (1,3) to the line 5x-12y+17=0 is
2a=|5×112×3+17|169=1413
Answer = 4a = 2813

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