Maharashtra State BoardHSC Science (Electronics) 11th
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If y = 2x is a chord of circle x2 + y2−10x = 0, find the equation of circle with this chord as diametre - Mathematics and Statistics

Sum

If y = 2x is a chord of circle x2 + y2−10x = 0, find the equation of circle with this chord as diametre

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Solution

The equation of the circle is

x2 + y2 − 10x = 0   ...(1)

and the equation of the line is y = 2x  ...(2)

Let A(x1, y1) and B(x2, y2) be the points of intersection of circle and the line.

To find the points of intersection, substitute y = 2x in 1 equation (1), we get,

x2 + 4x2 − 10x = 0

∴ 5x2 − 10x = 0

∴ x(5x − 10) = 0

∴ x = 0 or x = 2

∴ x1 = 0 and x2 = 2

Also, y1 = 2x1 and y2 = 2x2

∴ y1 = 0 and y2 = 4

∴ A ≡ (0, 0) and B ≡ (2, 4)

∴ by diameter form, the equation of the circle on chord AB as diameter is

(x − 0)(x − 2) + (y − 0)(y − 4) = 0

∴ x2 − 2x + y2 − 4y = 0

∴ x2 + y2 − 2x − 4y = 0.

  Is there an error in this question or solution?
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