Coordinate Geometry Question 97
Question: If the coordinates of a point be given by the equations $ x=b\sec \varphi ,\y=a\tan \varphi $ , then its locus is
Options:
A) A straight line
B) A circle
C) An ellipse
D) A hyperbola
Show Answer
Answer:
Correct Answer: D
Solution:
Here $ \frac{x}{b}=\sec \varphi $ and $ \frac{y}{a}=\tan \varphi $ Therefore $ \frac{x^{2}}{b^{2}}-\frac{y^{2}}{a^{2}}={{\sec }^{2}}\varphi -{{\tan }^{2}}\varphi \Rightarrow \frac{x^{2}}{b^{2}}-\frac{y^{2}}{a^{2}}=1 $ , which is obviously a hyperbola.
BETA
