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Find the two points on the parabola x^(...

Find the two points on the parabola `x^(2)=8y ` each of which is at a distance 4 unit from the focus. Find also the equation of the circle whose diameter is the line segment joining these two points .

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The correct Answer is:
`(x - 0 )^(2) +(y - 2)^(2) =4^(2)` or `x^(2) + y^(2) - 4y + 4 = 16 ` or `x^(2)+y^(2)-4y - 12 = 0 `
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