Conic Sections Question 513
Question: The point of contact of the tangent $ y=x+2 $ to the hyperbola $ 5x^{2}-9y^{2}=45 $ is
Options:
A) (9/2, 5/2)
B) (5/2, 9/2)
C) (-9/2, -5/2)
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Hyperbola is $ \frac{x^{2}}{9}-\frac{y^{2}}{5}=1 $ .
Hence point of contact is $ [ \frac{-9(1)}{\sqrt{9-5}},\frac{-5}{\sqrt{9-5}} ]\equiv [ \frac{-9}{2},\frac{-5}{2} ] $ .
Trick: Since the point $ ( -\frac{9}{2},-\frac{5}{2} ) $ satisfies both the equations.
BETA
