Conic Sections Question 406
Question: The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, -2). The equation of the hyperbola is
Options:
A) $ \frac{4}{49}x^{2}-\frac{196}{51}y^{2}=1 $
B) $ \frac{49}{4}x^{2}-\frac{51}{196}y^{2}=1 $
C) $ \frac{4}{49}x^{2}-\frac{51}{196}y^{2}=1 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Trick: $ 2a=7 $ or $ a=\frac{7}{2} $
Also (5, -2) satisfies it, so $ \frac{4}{49}(25)-\frac{51}{196}(4)=1 $
and $ a^{2}=\frac{49}{4} $
therefore $ a=\frac{7}{2} $ .
BETA
