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
Create a free account to view solution
View Solution FreeMore Parabola Questions
Let O be the vertex and Q be any point on the parabola, x2 = 8y. If the point P divides the line segment OQ internally i...If x + y = k is normal to y2 =12x , then k is...If a ≠ 0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x...Let the image of the parabola $x^2 = 4y$ in the line $x - y = 1$ be $(y + a)^2 = b(x - c)$, where $a, b, c \in \mathbb{N...Length of the normal chord of the parabola, y2 = 4x, which makes an angle of with the axis of x is -...