ParabolaHard
Question
The locus of a point such that two tangents drawn from it to the parabola y2 = 4ax are such that the slope of one is double the other is -
Options
A.y2 = 9/2 ax
B.y2 = 9/4 ax
C.y2 = 9ax
D.x2 = 4ay
Solution
Let the point be (h, k)
Now equation of tangent to the parabola y2 = 4ax
whose slope is m is
y = mx +
as it passes through (h, k)
∴ k = mh +
⇒ m2h - mk + a = 0
It has two roots m1, 2m1
∴ m1 + 2m1 =
, 2m1.m1 = 
m1 =
.... (i)
m12 =
.....(ii) from (i) & (ii)
⇒
⇒ k2 = 
h
Thus locus of point is y2 =
ax.
Now equation of tangent to the parabola y2 = 4ax
whose slope is m is
y = mx +
as it passes through (h, k)
∴ k = mh +
⇒ m2h - mk + a = 0It has two roots m1, 2m1
∴ m1 + 2m1 =
, 2m1.m1 = m1 =
.... (i)m12 =
.....(ii) from (i) & (ii)⇒
⇒ k2 = hThus locus of point is y2 =
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