Find the equation of the diameter of the circle x2 + y2 + 6x – 2y =

1.	Find the equation of the diameter of the circle x2 + y2 + 6x – 2y = 6 which when produced passes through the point (1, -2).
Answer» Given x² + y² + 6x – 2y – 6 = 0 & P (1, -2) centre = (-3, 1) Slope of the diameter = m = \(\frac{y_2 - y_1}{x_2 - x_1}\) = \(\frac{1 - (-2)}{-3 - 1}\)= \(\frac{3}{-4}\) ∴ Equation of the diameter with (1, -2) & m = \(\frac{-3}{4}\) y – y₁ = m(x – x₁) y + 2 = \(\frac{-3}{4}\)(x - 1) 4y + 8 = -3x + 3 ⇒ 3x + 4y + 5 = 0.

Find the equation of the diameter of the circle x2 + y2 + 6x – 2y = 6 which when produced passes through the point (1, -2).

Answer»

Given x² + y² + 6x – 2y – 6 = 0 & P (1, -2) centre = (-3, 1)

Slope of the diameter = m = \(\frac{y_2 - y_1}{x_2 - x_1}\) = \(\frac{1 - (-2)}{-3 - 1}\)= \(\frac{3}{-4}\)

∴ Equation of the diameter with (1, -2) & m = \(\frac{-3}{4}\)

y – y₁ = m(x – x₁)

y + 2 = \(\frac{-3}{4}\)(x - 1)

4y + 8 = -3x + 3

⇒ 3x + 4y + 5 = 0.

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Find the equation of the diameter of the circle x2 + y2 + 6x – 2y = 6 which when produced passes through the point (1, -2).

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