Find the equation of the circle which passes through the center of the circle $x^{2} + y^{2} + 8 x + 10 y - 7 = 0$ ans is concentric with the circle $2 x^{2} + 2 y^{2} - 8 x - 12 y - 9 = 0$ .

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Solution

$C_{1} : x^{2} + y^{2} + 8 x + 10 y - 7 = 0$

$C_{2} : x^{2} + y^{2} - 4 x - 6 y - 9 / 2 = 0$

$C_{3} : x^{2} + y^{2} + a x + b y + c_{1} = 0$

$C_{3}$ is concentric with $C_{2}$ .

$\Rightarrow C_{3} : x^{2} + y^{2} - 4 x - 6 y + c = 0$

Centre of $C_{1} : (- 4, - 5)$

$\Rightarrow (- 4)^{2} + (- 5)^{2} - 4 (- 4) - 6 (- 5) + c = 0$

$\Rightarrow 16 + 25 + 16 + 30 + c = 0$ .

$\Rightarrow c = - 87$ .

Therefore, equation of circle is
$x^{2} + y^{2} - 4 x - 6 y - 87 = 0$ .

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Similar questions

Find the equation of the circle which passes through the centre of the circle $x^{2} + y^{2} + 8 x + 10 y - 7 = 0$ and is concentric with the circle $2 x^{2} + 2 y^{2} - 8 x - 12 y - 9 = 0.$

Q. Equation of the circle which passes through the centre of the circle

x^{2} + y^{2} + 8 x + 10 y - 7 = 0

and is concentric with the circle

2 x^{2} + 2 y^{2} - 8 x - 12 y - 9 = 10

Q. The equation of the circle concentric with the circle

x^{2} + y^{2} + 8 x + 10 y - 7 = 0

and passing through the centre of the circle

x^{2} + y^{2} - 4 x - 6 y = 0

Q. The equation of the circle concentric with the circle

x^{2} + y^{2} + 8 x + 10 y - 7 = 0

and passing through the centre of the circle

x^{2} + y^{2} - 4 x - 6 y = 0

is-

Q. Find the equation of the circle concentric with the circle

x^{2} + y^{2} - 8 x - 12 y + 15 = 0

and passing through the point

(5, 4)

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Find the equation of the circle which passes through the center of the circlex2+y2+8x+10y−7=0 ans is concentric with the circle 2x2+2y2−8x−12y−9=0.

C1:x2+y2+8x+10y−7=0 C2:x2+y2−4x−6y−9/2=0 C3:x2+y2+ax+by+c1=0 C3 is concentric with C2. ⇒C3:x2+y2−4x−6y+c=0 Centre of C1:(−4,−5) ⇒(−4)2+(−5)2−4(−4)−6(−5)+c=0 ⇒16+25+16+30+c=0. ⇒c=−87. Therefore, equation of circle is x2+y2−4x−6y−87=0.

Find the equation of the circle which passes through the center of the circle $x^{2} + y^{2} + 8 x + 10 y - 7 = 0$ ans is concentric with the circle $2 x^{2} + 2 y^{2} - 8 x - 12 y - 9 = 0$ .