Conic Sections Question 436
Question: Locus of the point of intersection of straight lines $ \frac{x}{a}-\frac{y}{b}=m $ and $ \frac{x}{a}+\frac{y}{b}=\frac{1}{m} $ is
[MP PET 1991, 2003]
Options:
A) An ellipse
B) A circle
C) A hyperbola
D) A parabola
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{x}{a}-\frac{y}{b}=m $ ……(i) $ \frac{x}{a}+\frac{y}{b}=\frac{1}{m} $ ……(ii) Multiplying equation (i) and (ii), $ ( \frac{x}{a}-\frac{y}{b} )( \frac{x}{a}+\frac{y}{b} )=m.\frac{1}{m} $
$ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ , which is the equation of hyperbola.
BETA
