Let d y d x = a x - b y + a b x + c y + a , where a , b , c are constants. represent a circle passing through the point 2 , 5 . Then the shortest distance of the point 11 , 6 from this circle is

Step-by-step solution

Let equation of circle is x 2 + y 2 + 2 g x + 2 f y + c = 0 Differentiating above equation w.r.t x we get, ⇒ d y d x = - 2 x + 2 g 2 y + 2 f Now, comparing with d y d x = a x - b y + a b x + c y + a We get, b = 0 , a = - 2 , c = 2 ⇒ - 2 g = - 2 ⇒ g = 1 Also, 2 f = - 2 So, f = - 1 Now circle will be x 2 + y 2 + 2 x - 2 y + c = 0 its passes through 2 , 5 which will give c = - 23 so circle will be x 2 + y 2 + 2 x - 2 y - 23 = 0 centre C = - 1 , 1 and radius 5 Now P is 11 , 6 So minimum distance of P