Conic Sections Question 96
Question: If the line $ lx+my+n=0 $ is a tangent to the parabola $ y^{2}=4ax $ , then locus of its point of contact is
[RPET 1997]
Options:
A) A straight line
B) A circle
C) A parabola
D) Two straight lines
Show Answer
Answer:
Correct Answer: C
Solution:
Equation of tangent to parabola $ ty=x+at^{2} $ ……(i) Clearly, $ lx+my+n=0 $ is also a chord of contact of tangents. Therefore $ ty=x+at^{2} $ and $ lx+my+n=0 $ represents the same line.
Hence, $ \frac{1}{l}=-\frac{t}{m}=\frac{at^{2}}{n} $
therefore $ t=\frac{-m}{l},t^{2}=\frac{n}{la} $
Eliminating t, we get,
$ m^{2}=\frac{nl}{a} $ i.e., an equation of parabola.
BETA
