Equation of the circle cutting orthogonally the three circles x2+y2-2 x+3 y-7=0, x2+y2+5 x-5 y+9=0 and x2+y2+7 x-9 y+29=0 is

Question

Equation of the circle cutting orthogonally the three circles x2+y2-2 x+3 y-7=0, x2+y2+5 x-5 y+9=0 and x2+y2+7 x-9 y+29=0 is (A) x2+y2-16 x-18 y-4=0 (B) x2+y2-7 x+11 y+6=0 (C) x2+y2+2 x-8 y+9=0 (D) None of these

Tardigrade Admin · Accepted Answer

S 1- S 2=0 ⇒ 7 x -8 y +16=0 S 2- S 3=0 ⇒ 2 x -4 y +20=0 S 3- S 1=0 ⇒ 9 x -12 y +36=0 On solving centre (8,9) Length of tangent =√S1=√64+81-16+27-7=√149 =(x-8)2+(y-9)2=149 =x2+y2-16 x-18 y-4=0

Q. Equation of the circle cutting orthogonally the three circles $x^{2} + y^{2} - 2 x + 3 y - 7 = 0$ , $x^{2} + y^{2} + 5 x - 5 y + 9 = 0$ and $x^{2} + y^{2} + 7 x - 9 y + 29 = 0$ is

$x^{2} + y^{2} - 16 x - 18 y - 4 = 0$

$x^{2} + y^{2} - 7 x + 11 y + 6 = 0$

$x^{2} + y^{2} + 2 x - 8 y + 9 = 0$

None of these

Q. Equation of the circle cutting orthogonally the three circles x2+y2−2x+3y−7=0, x2+y2+5x−5y+9=0 and x2+y2+7x−9y+29=0 is

x2+y2−16x−18y−4=0

x2+y2−7x+11y+6=0

x2+y2+2x−8y+9=0

None of these

S1​−S2​=0⇒7x−8y+16=0 S2​−S3​=0⇒2x−4y+20=0 S3​−S1​=0⇒9x−12y+36=0 On solving centre (8,9) Length of tangent =S1​​=64+81−16+27−7​=149​ =(x−8)2+(y−9)2=149 =x2+y2−16x−18y−4=0

Q. Equation of the circle cutting orthogonally the three circles $x^{2} + y^{2} - 2 x + 3 y - 7 = 0$ , $x^{2} + y^{2} + 5 x - 5 y + 9 = 0$ and $x^{2} + y^{2} + 7 x - 9 y + 29 = 0$ is

$x^{2} + y^{2} - 16 x - 18 y - 4 = 0$

$x^{2} + y^{2} - 7 x + 11 y + 6 = 0$

$x^{2} + y^{2} + 2 x - 8 y + 9 = 0$