Let a line perpendicular to the line 2 x − y = 10 touch the parabola y 2 = 4 ( x − 9 ) at the point P . The distance of the point P from the centre of the circle x 2 + y 2 − 14 x − 8 y + 56 = 0 is ___

Question

Let a line perpendicular to the line 2 x − y = 10 touch the parabola y 2 = 4 ( x − 9 ) at the point P . The distance of the point P from the centre of the circle x 2 + y 2 − 14 x − 8 y + 56 = 0 is __________

TestHub · Accepted Answer

y 2 = 4 ( x − 9 ) slope of tangent = 2 − 1 ​ Point of contact P ( 9 + ( − 2 1 ​ ) 2 1 ​ , 2 − 1 ​ 2 × 1 ​ ) ​ P ( 13 , − 4 ) center of circle C ( 7 , 4 ) distance CP = ( 13 − 7 ) 2 + ( − 4 − 4 ) 2 ​ = 10 ​

Mathematics - Parabola Question with Solution | TestHub

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