If p and q be the longest and the shortest distance respectively of the point ( − 7 , 2 ) from any point ( α , β ) on the curve whose equation is x 2 + y 2 − 10 x − 14 y − 51 = 0 , then G.M. of p

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The centre C of the circle = ( 5 , 7 ) and the radius = 5 2 + 7 2 + 51 ​ = 5 5 ​ PC = 1 2 2 + 5 2 ​ = 13 ⇒ q = P A = 13 − 5 5 ​ and p = PB = 13 + 5 3 ​ ∴ G.M. of p and q = pq ​ = ( 13 − 5 5 ​ ) ( 13 + 5 5 ​ ) ​ = 169 − 125 ​ = 2 11 ​ .

Mathematics - Circle Question with Solution | TestHub

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