The vertex of the parabola ( y - 1 ) 2 = 8 ( x - 1 ) is at the centre of a circle and the parabola cuts that circle at the ends of its latus rectum. Then the equation of that circle is

Question

The vertex of the parabola ( y - 1 ) 2 = 8 ( x - 1 ) is at the centre of a circle and the parabola cuts that circle at the ends of its latus rectum. Then the equation of that circle is, x 2 + y 2 - 2 x - 2 y - 18 = 0, x 2 + y 2 - 2 x - 2 y + 18 = 0, x 2 + y 2 + 2 x + 9 y - 16 = 0, x 2 + y 2 - 2 x - 2 y + 16 = 0

MARKS App · Accepted Answer

( y - 1 ) 2 = 8 ( x - 1 ) Vertex → ( 1 , 1 ) Circle ( x - 1 ) 2 + ( y - 1 ) 2 = α 2 Extremities of Lotus rectum → ( 3 , 5 ) It satisfies circle 2 2 + 4 2 = α 2 ⇒ α 2 = 20 x 2 + y 2 - 2 x - 2 y - 18 = 0

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