Conic Sections Question 420
Question: A hyperbola passes through the points (3, 2) and (-17, 12) and has its centre at origin and transverse axis is along x-axis. The length of its transverse axis is
Options:
2
4
6
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let the equation of hyperbola is $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $
But it passes through (3, 2)
therefore $ \frac{9}{a^{2}}-\frac{4}{b^{2}}=1 $ ….. (i) Also it passes through (-17, 12)
therefore $ \frac{{{(-17)}^{2}}}{a^{2}}-\frac{{{(12)}^{2}}}{b^{2}}=1 $ …… (ii) Solving these, we get $ a=1 $ and $ b= \sqrt{2} $
Hence length of transverse axis $ =2a=4 $ .
BETA
