JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q30

← JEE Main 2022 · 29 Jul · Shift 1

MathematicsInteger+4 / -1Question 30 of 90

Let the mirror image of a circle $c_1:\ x^2+y^2-2x-6y+\alpha=0$ in line $y=x+1$ be $c_2:\ 5x^2+5y^2+10gx+10fy+38=0$ . If r is the radius of circle $c_2$ , then $\alpha+6r^2$ is equal to _______.

Your answer

Answer and worked solution

Official answer: 12

Centre. Reflecting in $y=x+1$ sends $(x,y)\to(y-1,x+1)$ : centre (1, 3) goes to (2, 2).

Radius. $c_2$ : $r^2=4+4-\frac{38}5=\frac25$ , and $10-\alpha=\frac25$ , so $\alpha=\frac{48}5$ .

Value $\frac{48}5+\frac{12}5=12$ .

Answer: 12

Topics:Equation of a circle Distance and section formulae

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JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 30