A tangent is drawn at the point $P (α, β)$ on the parabola $y^{2} = 4 a x$ . This tangent meets a second parabola $y^{2} = 4 a (x + k)$ at A and B, what is the midpoint of AB?

Q. If two tangents drawn from the point

(x_{1}, y_{1})

to the parabola

y^{2} = 4 x

be such that the slope of one tangent is double of the other, then

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If two tangents from the point (α,β) to the parabola y2=4x be such that the slope of one tangent is double of the other than

The correct option is B α=29β2y=mx+1m β=mα+1m αm2−αm+1=0 Roots m1,2m1 m1+2m1=βα,m1.2m1=1α 2(β3α)2=1α 2β2=9α

If two tangents from the point $(α, β)$ to the parabola $y^{2} = 4 x$ be such that the slope of one tangent is double of the other than

The correct option is B $α = \frac{2}{9} β^{2}$
$y = m x + \frac{1}{m}$ $β = m α + \frac{1}{m}$
$α m^{2} - α m + 1 = 0$ $R o o t s m_{1}, 2 m_{1}$
$m_{1} + 2 m_{1} = \frac{β}{α}, m_{1} .2 m_{1} = \frac{1}{α}$ $2 {(\frac{β}{3 α})}^{2} = \frac{1}{α}$ $2 β^{2} = 9 α$