If the tangent to the conic, y - 6 = x 2 at ( 2 , 10 ) touches the circle, x 2 + y 2 + 8 x - 2 y = k (for some fixed k ) at a point α , β ; then ( α , β ) is

Question

If the tangent to the conic, y - 6 = x 2 at ( 2 , 10 ) touches the circle, x 2 + y 2 + 8 x - 2 y = k (for some fixed k ) at a point α , β ; then ( α , β ) is, - 7 17 , 6 17, - 8 17 , 2 17, - 6 17 , 10 17, - 4 17 , 1 17

MARKS App · Accepted Answer

The equation of tangent ( T = 0 ) would be 1 2 y + 10 - 6 = 2 x 4 x - y + 2 = 0 The center of the circle is ( - 4 , 1 ) and the point of contact would be the foot of perpendicular from ( - 4 , 1 ) on 4 x - y + 2 = 0 α + 4 4 = β - 1 - 1 = - - 16 - 1 + 2 4 2 + 1 2 α + 4 4 = 15 17 and β - 1 - 1 = 15 17 α = - 8 17 , β = - 15 17 + 1 = 2 17 Hence option - 8 17 , 2 17 is correct.

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