If two tangents drawn from the point P ( h , k ) to the parabola y 2 = 8 x are such that the slope of one of the tangent is 3 times the slope of the other, then the locus of point P is

Question

If two tangents drawn from the point P ( h , k ) to the parabola y 2 = 8 x are such that the slope of one of the tangent is 3 times the slope of the other, then the locus of point P is, 3 y 2 = 16 x, 3 y 2 = 8 x, y 2 = 32 x, 3 y 2 = 32 x

MARKS App · Accepted Answer

Equation of tangent in slope form is y = m x + a m Let the tangent passes through P h , k ⇒ k = m h + a m ⇒ m 2 h - k m + a = 0 ⇒ m 1 + m 2 = k h & m 1 m 2 = a h Where, a = 2 & m 2 = 3 m 1 ⇒ 4 m 1 = k h & 3 m 1 2 = 2 h ⇒ 3 k 4 h 2 = 2 h ⇒ 3 y 2 = 32 x

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