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Question

Question: The locus of the point of intersection of two tangents to the parabola y<sup>2</sup> = 4ax which mak...

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make an angle 45o with one another is

A

3(y2- 4ax) = (x+a)2

B

y2 - 4ax = 3(x+a)2

C

y2 - 4ax = (x+a)2

D

y2 - 4ax = 2(x+a)2

Answer

y2 - 4ax = (x+a)2

Explanation

Solution

tanα = S11x1+a\frac{\sqrt{S_{11}}}{x_{1} + a}

tan450 = y124ax1x1+a\frac{\sqrt{y_{1}^{2} - 4ax_{1}}}{x_{1} + a}

The locus of (x1, y1) is y2 – 4ax = (x+a)2.