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A variable chord is drawn through the or...

A variable chord is drawn through the origin to the circle `x^2+y^2-2a x=0` . Find the locus of the center of the circle drawn on this chord as diameter.

Text Solution

Verified by Experts

The correct Answer is:
3

`t_(1)t_(2)=-4`
`h=(t_(1)^(2)+t_(2)^(2))/3, k=(2t_(1)+2t_(2))/3`
`3h=(t_(1)+t_(2))^(2)+8`
`3h=(9k^(2))/4 +8 implies y^(2)=1/9 (12x-32)`
`implies y^(2) =4/3 (x-8/3)`
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