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Question : 57 of 160
Marks:
+1,
-0
Solution:
Given, hyperbola,
9x2−16y2=144⇒‌‌(‌)2−(‌)2=1Here,
a=4 and
b=3∵‌‌a>b∴‌‌e=√1+‌=√1+‌=‌Asymptotes
y=±‌x=±‌xLatus rectums
x=±ae=±4(‌)=±5∵‌‌p>0∴ Consider the latus rectum
x=5The points of intersection of latus rectum
x=5 with asymptotes
y=±‌x are
(5,‌(5))‌ and ‌(5,−‌(5))∵‌q>0∴‌(p,q)=(5,‌)Therefore,
q=‌
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