Question
Question: The asymptotes of the hyperbola are 7x + 5y = 3 and 2x + 4y + 1 = 0. If it passes through (-2, 1) th...
The asymptotes of the hyperbola are 7x + 5y = 3 and 2x + 4y + 1 = 0. If it passes through (-2, 1) then its equation is
A
14x2 + 38xy +20y2 + x – 7y + 9 = 0
B
14x2 + 38xy +20y2 - x + 7y + 9 = 0
C
14x2 + 38xy +20y2 - 7x + y - 9 = 0
D
14x2 + 20y2 +38xy + x – 7y + 9 = 0
Answer
14x2 + 20y2 +38xy + x – 7y + 9 = 0
Explanation
Solution
Since equations of Hyperbola and Asymptotes differ by a constant. Let the equation of Hyperbola is
(7x + 5y- 3)(2x + 4y + 1) = λ
But it passes through (-2, 1) ⇒ λ = -12
∴ The equation of hyperbola is
14x2 + 20y2 +38xy + x – 7y + 9 = 0