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If a circle passes through the points of intersection of the coordinate axes with the lines ` lambdax-y + 1=0` and `x-2y + 3 = 0`, then the value of `lambda` is............

Text Solution

Verified by Experts

The correct Answer is:
`lambda=2 or -(1)/(2)`
Since, the point of intersection of the coordinate axes with the line `lambdax-y+1=0 and x-2y + 3 =0` forms the circle.
`therefore (lambdax-y+1)(x-2y+3)=0`
represents a circle, if coefficient of `x^(2)="coefficient " of y^(2) and "cofficient of" xy=0 `
`rArr lambda=2or-2lambda-1=0`
`rArr lambda=2 or lambda=-(1)/(2)`
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