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Question

If tangents are drawn to the parabola (x2)2+(y3)2=(3x+4y5)225 at the extremities of the chord 3xy3=0, then angle between the tangents is

A
45
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B
90
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C
60
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D
120
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Solution

The correct option is B 90
Given parabola is
(x2)2+(y3)2=(3x+4y5)225

General equation of parabola whose focus is (α,β) and directix equation ax+by+c=0 is
(xα)2+(yβ)2=(ax+by+c)2a2+b2
Comparing the given parabola, we get
FocusS(α,β)(2,3)
Equation of directrix as
3x+4y5=0

Given line is 3xy3=0, which passes through (2,3)
So, the given chord is a focal chord

Therefore, the tangents drawn at the extremities of focal chord are perpendicular.

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