Question

The centre of the circle passing through the points (0 0) (1 0)

Answer 1

Step-by-step explanation:

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Find centre of circle passing through (0,0) and (1,0) ....

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Let us consider General equation of circle..

${x}^{2} + {y}^{2} + 2gx + 2fy + c = 0 \\ \\ where.. \\ centre = ( - g, - f)$

If it passes through (0,0) it will satisfy its equation....

${0}^{2} + {0}^{2} +0 + 0 + c = 0 \\ \\ \implies c = 0........(1)$

If it passes through (1,0) it will also satisfy its equation...

$1 {}^{2} + {0}^{2} + 2g(1) + 0 + c = 0 \\ \\ 1 + 2g + c = 0 \\ \\ 1 + 2g = 0..........(as \: \: c = 0) \\ \\ g = - \frac{ 1}{2} \\ \\ f = 0 \\ \\ now \: \: centre \: \: is \: \: ( - g, - f) \\ \\ \huge \boxed{centre \implies ( \frac{1}{2},0) }$