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Circle drawn having its diameter equal to the focal distance of any point lying on the parabola `x^2-4x+6y+10=0` will touch a fixed line. Find its equation.

Text Solution

Verified by Experts

The correct Answer is:
y+1=0
`x^(2)-4x+6y+10=0`
`or" "x^(2)-4x+4=-6-6y`
`or" "(x-2)^(2)=-6(y+1)`
The circle drawn on focal distance as diameter always touches the tangent drawn to the parabola at vertex.
Thus, the circle will touch the line y+1=0.
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