Tangents from the Center

★ 7/10Circles conic sections analytic geometry Vieta's Formulas

Problem

Let $P(a, b)$ be any point on the ellipse $\dfrac{x^2}{3} + \dfrac{y^2}{2} = 1$ . From the origin $O$ , two tangent lines to the circle

(x - a)^2 + (y - b)^2 = \frac{6}{5} \qquad \left(a^2 \neq \frac{6}{5}\right)

are drawn, meeting the ellipse at points $M$ and $N$ . Find the product of the slopes of $OM$ and $ON$ .

Answer

Solution

Difficulty	7/10
Topics	Circles, conic sections, analytic geometry, Vieta's Formulas

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