Conic Sections Question 140
Question: If the segment intercepted by the parabola $ y^{2}=4ax $ with the line $ lx+my+n=0 $ subtends a right angle at the vertex, then
Options:
A) $ 4al+n=0 $
B) $ 4al+4am+n=0 $
C) $ 4am+n=0 $
D) $ al+n=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
The combined equation of the lines joining the vertex to the points of intersection of the line $ lx+my+n=0 $ and the parabola $ y^{2}=4ax $ , is $ y^{2}=4ax( \frac{lx+my}{-n} ) $ or $ 4alx^{2}+4amxy+ny^{2}=0 $
This represents a pair of perpendicular lines, if $ 4al+n=0 $ .
BETA
