Question
Question: The straight line x + y = \(\sqrt{2}p\)will touch the hyperbola 4x<sup>2</sup> –9y<sup>2</sup> = 36,...
The straight line x + y = 2pwill touch the hyperbola 4x2 –9y2 = 36, if
A
p2 = 2
B
p2 = 5
C
5p2 = 2
D
2p2 = 5
Answer
2p2 = 5
Explanation
Solution
4x2 –9y2 = 36
Ž 9x2– 4y2= 1
line x + y = 2p
Ž y = –x + 2p
Condition of tangency c = ± a2m2−b2
Ž2p = ± 9(−1)2−4 Ž 2p2 = 5