Number of circles intersecting x^2+y^2=4,x^2+ | vedclass

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

Question

(A) Let the required circle be $S \equiv x^2+y^2+2gx+2fy+c=0$. For a circle to be orthogonal to $x^2+y^2+2g_i x+2f_i y+c_i=0$,the condition is $2gg_i+

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Let the required circle be $S \equiv x^2+y^2+2gx+2fy+c=0$. For a circle to be orthogonal to $x^2+y^2+2g_i x+2f_i y+c_i=0$,the condition is $2gg_i+2ff_i=c+c_i$. Given circles: $S_1: x^2+y^2-4=0 \Rightarrow g_1=0, f_1=0, c_1=-4$ $S_2: x^2+y^2-2x-3=0 \Rightarrow g_2=-1, f_2=0, c_2=-3$ $S_3: x^2+y^2-2y-3=0 \Rightarrow g_3=0, f_3=-1, c_3=-3$ Applying the condition: $1$) For $S_1$: $2g(0)+2f(0)=c-4 \Rightarrow c=4$. $2$) For $S_2$: $2g(-1)+2f(0)=c-3$ $\Rightarrow -2g=4-3=1$ $\Rightarrow g=-1/2$. $3$) For $S_3$: $2g(0)+2f(-1)=c-3$ $\Rightarrow -2f=4-3=1$ $\Rightarrow f=-1/2$. Now,check the radius $r$ of the circle $S$: $r^2 = g^2+f^2-c = (-1/2)^2+(-1/2)^2-4 = 1/4+1/4-4 = 1/2-4 = -7/2$. Since $r^2 Thus,the number of such circles is $0$.

Number of circles intersecting $x^2+y^2=4$,$x^2+y^2-2x-3=0$ and $x^2+y^2-2y-3=0$ orthogonally is

Similar Questions

If the circles $x^2 + y^2 - 2ax + c = 0$ and $x^2 + y^2 + 2by + 2\lambda = 0$ intersect orthogonally,then the value of $\lambda$ is

The radius of the circle whose centre lies at $(1, 2)$,while cutting the circle $x^2 + y^2 + 4x + 16y - 30 = 0$ orthogonally,is (in units):

The length of the diameter of the circle which cuts the following three circles orthogonally is:
$x^{2}+y^{2}-x-y-14=0$
$x^{2}+y^{2}+3x-5y-10=0$
$x^{2}+y^{2}-2x+3y-27=0$

Find the equation of a circle with radius $3$ that touches the circle $x^{2} + y^{2} - 4x - 6y - 12 = 0$ internally at the point $(-1, -1)$.

$A$ circle $C$ touches the line $x=2y$ at the point $(2,1)$ and intersects the circle $C_{1}: x^{2}+y^{2}+2y-5=0$ at two points $P$ and $Q$ such that $PQ$ is a diameter of $C_{1}$. Then the diameter of $C$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module