Find the equation of the circle with centre at $(3, - 1)$ and which cuts off a chord of length $6$ on the line $2 x - 5 y + 18 = 0$

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Solution

We have
$2 x - 5 y + 18 = 0$
$A P$ (Length of perpendicular force $
$\frac{12 \times 3 - 5 (- 1) + 81}{\sqrt{4 + 25}} = \sqrt{29}$

$r = A B = \sqrt{9 + {(A P)}^{2}} = \sqrt{38}$
${(x - 3)}^{2} - (y + 1) = 38$
Hence, the equation of the circle is
$x^{2} + y^{2} - 6 x + 2 y = 28$

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Similar questions

Find the equation of a circle whose centre is (3, -1) and which cuts off a chord of length 6 units on the line $2 x - 5 y + 18 = 0$ .

Find the equation of the circle whose centre is (3, -1) and which cut-off an intercept of length 6 from the line $2 x - 5 y + 18 = 0$ .

(3, - 1)

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2 x - 5 y + 18 = 0

(3, - 1)

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2 x - 5 y + 18 = 0

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2 x - 5 y + 18 = 0

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