Question

If y=2x be the equation to the chord of a circle
circle X2 + y2 = 10x .Find
the equation to the circle of which this chord is a diameter.

Answer 1

Answer:

hey here is your solution

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Step-by-step explanation:

$so \: here \: for \: a \: certain \: circle \: \\ y = 2x \: is \: equation \: of \: chord \: to \: a \: circle \: x {}^{2} + y {}^{2} = 10 x\\ so \: substituting \: value \: of \: y \: in \: x {}^{2} + y {}^{2} = 10 x\\ we \: get \\ x {}^{2} + (2x) {}^{2} = 10x \\ x {}^{2} + 4x {}^{2} = 10x \\ 5x {}^{2} = 10x \\ 5x {}^{2} - 10x = 0 \\ 5x(x - 2) = 0 \\ ie \: \: \: 5x = 0 \: \: or \: \: x - 2 = 0 \\ so \: hence \\ x = 0 \: \: or \: \: x = 2 \\ \\ substitute \: values \: of \: x \: in \: y = 2x \\ we \: get \\ y = 0 \: \: or \: \: y = 4$

$so \: these \: two \: values \: of \: x \: and \: y \: are \: nothing \: but \: their\: 2 \: coordinates \: ie \: \\ (x1 \: and \: x2) \: and \:( y1 \: ad \: y2) \\ so \: let \: then \\ (x1,y1) = (0,0) \\ (x2,y2) = (2,4) \\ \\ now \: we \: know \: that \\ diameter \: equation \: form \: of \: circle \: is \: given \: by \\ (x - x1)(x - x2) + (y -y1)(y - y2) = 0 \\ (x - 0)(x - 2) + (y - 0)(y - 4) = 0 \\ x(x - 2) + y(y - 4) = 0 \\ x {}^{2} - 2x + y {}^{2} - 4y = 0 \\ ie \: \: x {}^{2} + y {}^{2} - 2x - 4y = 0 \\ \\ hence \: equation \: circle \: is \: x {}^{2} + y {}^{2} - 2x - 4y = 0$