Conic Sections Question 484
Question: Find the equation of axis of the given hyperbola $ \frac{x^{2}}{3}-\frac{y^{2}}{2}=1 $ which is equally inclined to the axes
[DCE 2005]
Options:
A) $ y=x+1 $
B) $ y=x-1 $
C) $ y=x+2 $
D) $ y=x-2 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{x^{2}}{3}-\frac{y^{2}}{2}=1 $
$ \because $ Equation of tangent are equally inclined to the axis i.e., $ \tan \theta =1=m $ . Eq. of tangent $ y=mx+\sqrt{a^{2}m^{2}-b^{2}} $
Given eq. $ \frac{x^{2}}{3}-\frac{y^{2}}{2}=1 $ is a eq. of hyperbola which is of form $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ . Now, on comparing $ a^{2}=3 $ , $ b^{2}=2 $
$ y=1.x+\sqrt{3\times {{(1)}^{2}}-2} $
therefore $ y=x+1 $ .
BETA
