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Question

If tangents are drawn to the parabola (x3)2+(y+4)2=(3x4y6)225 at the extremities of the chord 2x3y18=0, then angle between 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
(x3)2+(y+4)2=(3x4y6)225
The 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 with the standard parabola,we get
Focus S(α,β)(3,4)

As (3,4) satisfies 2x3y18=0
So, the given chord is focal chord

Tangents drawn at the extremities of focal chord are perpendicular and intersect at directrix so the angle is 90

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