Question
Mathematics Question on Hyperbola
Let P(x0,y0) be the point on the hyperbola 3x2−4y2=36, which is nearest to the line 3x+2y=1 Then 2(y0−x0) is equal to :
A
-9
B
3
C
9
D
-3
Answer
-9
Explanation
Solution
3x2−4y2=36
3x+2y=1
m=−23
m=+12 tan θ3 sec θ
⇒m = 123 × sin θ1 = −23
sinθ =−31
(12⋅sec θ, 3tan θ)
(12⋅23, −3×21) ⇒ (26, −23)
Now,
2(y0−x0) = 2 (- 23 - 26 ) = - 3 - 6 = - 9
So, the correct option is (A): - 9