If one of the diameters of the circle, given by the equation, x2 + y2 – 4x + 6y – 12 = 0, is a chord of a circle S, whose centre is at (

Engineering

Mathematics

A Circle

Question

If one of the diameters of the circle, given by the equation, x² + y² – 4x + 6y – 12 = 0, is a chord of a circle S, whose centre is at (– 3, 2), then radius of S is

$5 \sqrt{2}$

$5 \sqrt{3}$

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C₁ (2, – 3)

$r_{1} = \sqrt{4 + 9 + 12} = 5$

${CC}_{1} = \sqrt{5^{2} + 5^{2}} = 5 \sqrt{2}$

R² = 25 + 50 = 75

$R = 5 \sqrt{3} .$