If p and q be the longest and the shortest distances respectively of the point ( − 7 , 2 ) from any point ( α , β ) on the circle x 2 + y 2 − 10 x − 14 y − 51 = 0 . Then the geometric mean of p and q

Question

If p and q be the longest and the shortest distances respectively of the point ( − 7 , 2 ) from any point ( α , β ) on the circle x 2 + y 2 − 10 x − 14 y − 51 = 0 . Then the geometric mean of p and q is equal to

TestHub · Accepted Answer

Centre of the circle is C ( 5 , 7 ) . Let P ( − 7 , 2 ) be the given point and the line joining P and C meet the circle at A and B Now PC = ( 12 ) 2 + ( 5 ) 2 ​ = 13 radius of the circle is 5 2 + 7 2 + 51 ​ = 5 5 ​ p = PB = 13 + 5 5 ​ , q = P A = 13 − 5 5 ​ G M of p , q = pq ​ = ( 13 ) 2 − ( 5 5 ​ ) 2 ​ = 2 11 ​ = 6.63

Mathematics - Circle Question with Solution | TestHub

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JEE Advanced (2028)