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Question

The equation of parabola whose focus is (5,3) and directrix is 3x4y+1=0, is

A
(4x+3y)2256x142y+849=0
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B
(4x3y)2256x142y+849=0
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C
(3x+4y)2142x256y+849=0
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D
(3x4y)2256x142y+849=0
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Solution

The correct option is A (4x+3y)2256x142y+849=0
Let P(h,k) be the point on required parabola
By definition
SP=PM
(5h)2+(k3)2=|3h4k+1|(3)2+(4)2
25(5h)2+25(k3)2=(3h4k+1)2
16h2256h+9k2142k+24hk+849=0
(4h+3k)2256h142k+849=0

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