Conic Sections Question 294
Question: The equation of the tangent parallel to $ y-x+5=0 $ drawn to $ \frac{x^{2}}{3}-\frac{y^{2}}{2}=1 $ is
[UPSEAT 2004]
Options:
A) $ x-y-1=0 $
B) $ x-y+2=0 $
C) $ x+y-1=0 $
D) $ x+y+2=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Given hyperbola is, $ \frac{x^{2}}{3}-\frac{y^{2}}{2}=1 $ ……(i) Equation of tangent parallel to $ y-x+5=0 $ is $ y-x+\lambda =0 $
$ \Rightarrow $ $ y=x-\lambda $ ……(ii) If line (ii) is a tangent to hyperbola (i), then $ -\lambda =\pm \sqrt{3\times 1-2} $ (from $ c=\pm \sqrt{a^{2}m^{2}-b^{2}} $ ) $ -\lambda =\pm 1\Rightarrow \lambda =-1,+1 $ . Put the values of $ \lambda $ in (ii), we get $ x-y-1=0 $ and $ x-y+1=0 $ are the required tangents.
BETA
