Find the equation of the circle passing through the point of intersection of the lines `x+3y=0\ a n d\ 2x-7y=0` and whose centre is the point of intersection of the lines `x+y+1=0\ a n d\ x-2y+4=0.`

Explanation

The point of intersection of the lines `x+3 y=0` and `2 x-7 y=0` is `(0,0)`.

Let `(h, k)` be the centre of a circle with radius `a`.

Thus, its equation will be

`(x-h)^{2}+(y-k)^{2}=a^{2}`

The point of intersection of the lines `x+y+1=0` and `x-2 y+4=0` is `(-2,1)`.

`therefore h=-2, k=1`

`therefore` Equation of the required circle `=(x+2)^{2}+(y-1)^{2}=a^{2} ldots(1)`

Also, equation (1) passes through `(0,0)`.

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