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the equation of the circle with chord 2x=y of the circle x^2+y^2=10x as it's diameter
Asked by banuri06 | 07 Mar, 2022, 22:12: PM
Expert Answer
The chord and circle will intersect at two points.
When y = 2x, we have
x2 + (2x)2 = 10x
5x2 = 10x
5x(x - 2) = 0
Therefore, x = 0, 2
So, y = 0, 4
Thus, the points of intersection will be (0, 0) and (2, 4).
So, the end points of the diameter are (0, 0) and (2, 4)
Therefore, the equation of circle will be
(x - 0)(x - 2) + (y - 0)(y - 4) = 0
x2 - 2x + y2 - 4y = 0
x2 + y2 - 2x - 4y = 0
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