Conic Sections Question 474
Question: The locus of a point $ P(\alpha ,\beta ) $ moving under the condition that the line $ y=\alpha x+\beta $ is a tangent to the hyperbola $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ is
[AIEEE 2005]
Options:
A) A parabola
B) A hyperbola
C) An ellipse
D) A circle
Show Answer
Answer:
Correct Answer: B
Solution:
If $ y=mx+c $ is tangent to the hyperbola then $ c^{2}=a^{2}m^{2}-b^{2} $ . Here $ {{\beta }^{2}}=a^{2}{{\alpha }^{2}}-b^{2} $ .
Hence locus of P(a, b) is $ a^{2}x^{2}-y^{2}=b^{2} $ , which is a hyperbola.
BETA
