Conic Sections Question 138
Question: The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola $ y^{2}=8x $ , is
[MNR 1976]
Options:
A) $ \frac{1}{2}\sqrt{41} $
B) $ \sqrt{41} $
C) $ \frac{3}{2}\sqrt{41} $
D) $ 2\sqrt{41} $
Show Answer
Answer:
Correct Answer: C
Solution:
Equation of chord of contact of tangent drawn from a point $ ({x _{1,}}y_1) $ to parabola $ y^{2}=4ax $ is $ yy_1=2a(x+x_1) $ so that $ 5y=2\times 2(x+2) $
therefore $ 5y=4x+8. $ Point of intersection of chord of contact with parabola $ y^{2}=8x $ are $ ( \frac{1}{2},2 ),(8,8) $ , so that length $ =\frac{1}{2}\sqrt{41} $ .
BETA
