Question
Question: If m<sub>1</sub> and m<sub>2</sub> are the gradients of tangents to hyperbola \(\frac{x^{2}}{25} - \...
If m1 and m2 are the gradients of tangents to hyperbola 25x2−16y2=1 which passes through (6, 2), then-
A
m1 + m2 = 42/11
B
m1m2 = 20/11
C
m1+ m2 = 48/11
D
m1m2 = 11/20
Answer
m1m2 = 20/11
Explanation
Solution
25x2 – 16y2 = 1
equation of tangent in slope
y = mx ± 25m2−16
It passes through (6, 2)
\ 2 = 6m ± 25m2 – 16
(2 – 6m)2 = 25m2 – 16
4 + 36m2 – 24m = 25m2 – 16
11m2 – 24m + 20 = 0
m1 + m2 = 24/11, m1m2 = 20/11