Let a circle passing through ( 2 , 0 ) have its centre at the point ( h , k ) . Let ( x c , y c ) be the point of intersection of the lines 3 x + 5 y = 1 and ( 2 + c ) x + 5 c 2 y = 1 . If h = lim

Question

Let a circle passing through ( 2 , 0 ) have its centre at the point ( h , k ) . Let ( x c ​ , y c ​ ) be the point of intersection of the lines 3 x + 5 y = 1 and ( 2 + c ) x + 5 c 2 y = 1 . If h = lim c → 1 ​ x c ​ and k = lim c → 1 ​ y c ​ , then the equation of the circle is :

TestHub · Accepted Answer

​ ( 2 + c ) x + 5 c 2 ( 5 1 − 3 x ​ ) = 1 x = 2 + c − 3 c 2 1 − c 2 ​ , y = 5 1 − 3 x ​ = 5 ( 2 + c − 3 c 2 ) c − 1 ​ h = c → 1 lim ​ ( 1 − c ) ( 2 + 3 c ) ( 1 − c ) ( 1 + c ) ​ = 5 2 ​ K = c → 1 lim ​ − 5 ( c − 1 ) ( 3 c + 2 ) c − 1 ​ = − 25 1 ​ Centre ( 25 2 ​ , − 25 1 ​ ) ​ ​ r = ( 2 − 5 2 ​ ) 2 + ( 0 − 25 1 ​ ) 2 ​ = 25 64 ​ + 625 1 ​ ​ r = 25 161 ​ ​ ( x − 5 2 ​ ) 2 + ( y + 25 1 ​ ) 2 = 125 161 ​ ⇒ 25 x 2 + 25 y 2 − 20 x + 2 y − 60 = 0 ​

Mathematics - Circle Question with Solution | TestHub

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