Equation of circle which passes through origin, has its centre on line x + y = 4 and cuts circle {x^

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10-1.Circle and System of Circles

hard

The equation of the circle which passes through the origin, has its centre on the line $x + y = 4$ and cuts the circle ${x^2} + {y^2} - 4x + 2y + 4 = 0$ orthogonally, is

A

${x^2} + {y^2} - 2x - 6y = 0$

B

${x^2} + {y^2} - 6x - 3y = 0$

C

${x^2} + {y^2} - 4x - 4y = 0$

D

None of these

Solution

(c) Equation of circle with centre $( – g,\; – h)$ and passing through origin is

${x^2} + {y^2} + 2gx + 2fy = 0$….$(i)$

and $g + h + 4 = 0$….$(ii)$

Also $ – 4g + 2f = 4$….$(iii)$

$(ii)$ and $(iii)$ give $g$ and $f$, which will give the desired equation

${x^2} + {y^2} – 4x – 4y = 0$.

Standard 11

Mathematics

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