The general solution of the differential equation of all circles having centre at A (-1 ,2 ) is

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Accepted Answer

Correct answer: D. (d) : General equation of all circles having centre at A (-1 ,2 ) is (x+1 )^2+ (y-2 )^2=r^2; where r= radius of circles ⇒x^2+1+2x+y^2+4-4y=r^2 On differentiating w.r.t. ' x ', we get 2x+2+2y dy dx-4 dy dx=0 ⇒ dy dx (2y-4 )=-2x-2 ⇒ (2y-4 ) dy= (-2x-2 ) dx ⇒ 2 ydy- 4 dy= -2 xdx- 2 dx ⇒y^2-4y=-x^2-2x-c ⇒x^2+y^2+2x-4y+c=0

$The general solution of the differential equation of all circles having centre at A (- 1, 2) is$

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