JEE Advanced 2015 Paper 1 Mathematics Q15

Mathematics

Problem

Consider the family of all circles whose centers lie on the straight line

y=x

. If this family of circles is represented by the differential equation

Py''+Qy'+1=0

, where

P,Q

are functions of

x,y

and

y'

(here

y'=\frac{dy}{dx}

y''=\frac{d^2y}{dx^2}

), then which of the following statements is (are) true?