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Question: The number of normals to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ from an external point is...

The number of normals to the hyperbola x2a2−y2b2=1\frac{x^2}{a^2}-\frac{y^2}{b^2}=1 from an external point is

A

2

B

3

C

4

D

5

Answer

4

Explanation

Solution

From any point, the number of normals that can be drawn to a central conic (ellipse or hyperbola) is at most 4. For a hyperbola, the number of normals from an external point can be 2 or 4. The question asks for "The number of normals", implying a general case. For a general external point, the maximum number of normals is 4.