The equation of the circle passing through th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the equation of the circle be $S \equiv x^2+y^2+2gx+2fy=0$ (since it passes through the origin $(0,0)$).For the circle $S_1 \equiv x^2+y^2+6x-

Vedclass · Accepted Answer

$2x^2+2y^2-10x+5y=0$

Vedclass · Answer

(B) Let the equation of the circle be $S \equiv x^2+y^2+2gx+2fy=0$ (since it passes through the origin $(0,0)$).For the circle $S_1 \equiv x^2+y^2+6x-15=0$,we have $2g_1=6, 2f_1=0, c_1=-15$. The condition for orthogonality is $2gg_1+2ff_1=c+c_1$,which gives $2g(3)+2f(0)=0-15$ $\Rightarrow 6g=-15$ $\Rightarrow g=-\frac{5}{2}$.For the circle $S_2 \equiv x^2+y^2-8y-10=0$,we have $2g_2=0, 2f_2=-8, c_2=-10$. The condition for orthogonality is $2gg_2+2ff_2=c+c_2$,which gives $2g(0)+2f(-4)=0-10$ $\Rightarrow -8f=-10$ $\Rightarrow f=\frac{5}{4}$.Substituting $g$ and $f$ into the equation $S$,we get $x^2+y^2+2(-\frac{5}{2})x+2(\frac{5}{4})y=0$.Multiplying by $2$,we get $2x^2+2y^2-10x+5y=0$.

The equation of the circle passing through the origin and cutting the circles $x^2+y^2+6x-15=0$ and $x^2+y^2-8y-10=0$ orthogonally is

Similar Questions

$A$ circle $S$ passes through the points of intersection of the circles $x^2+y^2-2x-3=0$ and $x^2+y^2-2y=0$. If $x+y+1=0$ is a tangent to the circle $S$,then the equation of $S$ is

$A$ circle $S$ cuts three circles $x^2+y^2-4x-2y+4=0$,$x^2+y^2-2x-4y+1=0$,and $x^2+y^2+4x+2y+1=0$ orthogonally. Then,the radius of $S$ is

The equation of the circle passing through the point $(1, 1)$ and the points of intersection of $x^{2}+y^{2}-6x-8=0$ and $x^{2}+y^{2}-6=0$ is

If a diameter of the circle $x^2+y^2-4x+6y-12=0$ is a chord of a circle $S$ whose centre is at $(-3, 2)$,then the radius of $S$ is

The equation of a circle passing through the points of intersection of the circles $x^2 + y^2 + 13x - 3y = 0$ and $2x^2 + 2y^2 + 4x - 7y - 25 = 0$ and the point $(1, 1)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module