Question
Question: The value of m, for which the line y = mx + \(\frac{25\sqrt{3}}{3}\), is a normal to the conic \(\fr...
The value of m, for which the line y = mx + 3253, is a normal to the conic 16x2−9y2 = 1, is
A
3
B
–2/3
C
-23
D
1
Answer
–2/3
Explanation
Solution
We know that the equation of the normal of the conic a2x2−b2y2 = 1 at point ( a sec θ, b tan θ) is
Ax sec θ + bycot θ = a2 + b2
Or y = b−asin θ x + bcotθa2+b2
Comparing above equation with equation y = mx + 3253 and taking a = 4, b = 3
We get, bcotθa2+b2=3253⇒ tan θ = 3⇒ θ = 600
And m = - basin θ = 3−4sin 600 = 3−4x23=3−2.