Conic Sections Question 120
Question: The point of intersection of tangents at the ends of the latus-rectum of the parabola $ y^{2}=4x $ is equal to
[Pb. CET 2003]
Options:
A) (1, 0)
B) (-1, 0)
C) (0, 1)
D) (0, -1)
Show Answer
Answer:
Correct Answer: B
Solution:
Equation of the tangent at $ (x_1,y_1) $ on the parabola $ y^{2}=4ax $ is $ yy_1=2a(x+x_1) $
$ \therefore $ In this case, $ a=1 $
The co-ordinates at the ends of the latus rectum of the parabola $ y^{2}=4x $ are $ L(1,2) $ and $ L_1(1,-2) $
Equation of tangent at L and $ L_1 $ are $ 2y=2(x+1) $ and $ -2y=2(x+1) $ , which gives $ x=-1 $ , $ y=0 $ . Thus, the required point of intersection is (-1, 0).
BETA
