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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 12

Let dydx=ax−by+abx+cy+a\dfrac{dy}{dx}=\dfrac{ax-by+a}{bx+cy+a}, a,b,c∈Ra,b,c\in\mathbf R, represents a circle with center (α,β)(\alpha,\beta). Then, α+2β\alpha+2\beta is equal to :

Choose one option
Answer and worked solution

Official answer: C

Exact equation. (bx+cy+a)dy−(ax−by+a)dx=0(bx+cy+a)dy-(ax-by+a)dx=0 integrates to −a2x2+bxy−ax+c2y2+ay=k-\frac a2x^2+bxy-ax+\frac c2y^2+ay=k. A circle needs b=0b=0, c=−ac=-a: x2+y2+2x−2y=k′x^2+y^2+2x-2y=k'.

Centre (−1,1)(-1,1): α+2β=1\alpha+2\beta=1.

(C)

Topics:Formation and applicationsEquation of a circle
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