The difference of the focal distances of any point on the hyperbola is equal to its

Question

Let C be the circle $x^2+y^2+4x-6y-3=0$ and $L$ be the locus of the point of intersection of a pair of tangents to $C$ with the angle between the two tangents equal to $60º$ . Then, the point at which $L$ touches the line $x = 6$ is

Answer 1

Step 1: Basic Principle
For hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, foci are $(\pm ae, 0)$.
Step 2: Solution Procedure:
For any point $P(x,y)$ on hyperbola, $|PF_1 - PF_2| = 2a$, which is the length of the transverse axis.
Step 3: Required Answer:
The difference of focal distances equals the length of the transverse axis.

The difference of the focal distances of any point on the hyperbola is equal to its

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The Correct Option is C

Solution and Explanation

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