A Circle Cuts an Asymptote

★ 7/10Circles Power of a Point conic sections

Problem

The hyperbola $C:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ ( $a,b>0$ ) has right vertex $A$ . The circle centered at $A$ with radius $b$ meets one asymptote of $C$ at two points $M$ and $N$ , and

\overrightarrow{OM}=5\overrightarrow{ON},

where $O$ is the origin. Find the eccentricity of the hyperbola.

Answer

Solution

Difficulty	7/10
Topics	Circles, Power of a Point, conic sections

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