ParabolaHard
Question
Tangents are drawn from the point (-1, 2) on the parabola y2 = 4x. The length, these tangents will intercept on the line x = 2 :
Options
A.6
B.6√2
C.2√6
D.none of these
Solution
Let slope of tangent be m
So equation of tangent is
y = mx +
Now tangent passes through (-1, 2) so
⇒ m2 + 2m - 1 = 0
⇒ m = - 1 ± √2
equation of tangents are
y = ( -1 + √2) x +
....(i)
y = (-1 - √2)x -
....(ii)
intercept of tangent (i) & (ii) on line x = 2 is
y1 = 3√2 - 1 & y2 = - 3√2 - 1 respectively.
Now y1 - y2 is 6√2
So equation of tangent is
y = mx +
Now tangent passes through (-1, 2) so
⇒ m2 + 2m - 1 = 0
⇒ m = - 1 ± √2
equation of tangents are
y = ( -1 + √2) x +
....(i)y = (-1 - √2)x -
....(ii)intercept of tangent (i) & (ii) on line x = 2 is
y1 = 3√2 - 1 & y2 = - 3√2 - 1 respectively.
Now y1 - y2 is 6√2
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