Two Circles and a Far Line

★ 8/10Circles conic sections analytic geometry Vieta's Formulas

Problem

Let $P$ be an intersection point of the circles

O_1 \colon (x - a)^2 + (y - b)^2 = b^2 + 1, \qquad O_2 \colon (x - c)^2 + (y - d)^2 = d^2 + 1,

where $ac = 8$ and $\dfrac{a}{b} = \dfrac{c}{d}$ . Find the minimum distance between $P$ and a point $Q$ on the line $l \colon 3x - 4y - 25 = 0$ .

Answer

Solution

Difficulty	8/10
Topics	Circles, conic sections, analytic geometry, Vieta's Formulas

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