The equation of the circle which passes throu | vedclass

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

Question

(C) Let the required equation of the circle be $x^2+y^2+2gx+2fy=0$ (since it passes through the origin,$c=0$).For the circle $x^2+y^2+2g_1x+2f_1y+c_1=

Vedclass · Accepted Answer

$3x^2+3y^2-8x+29y=0$

Vedclass · Answer

(C) Let the required equation of the circle be $x^2+y^2+2gx+2fy=0$ (since it passes through the origin,$c=0$).For the circle $x^2+y^2+2g_1x+2f_1y+c_1=0$ to cut $x^2+y^2+2g_2x+2f_2y+c_2=0$ orthogonally,the condition is $2g_1g_2+2f_1f_2=c_1+c_2$.For the first circle $x^2+y^2-6x+8=0$,we have $g_1=-3, f_1=0, c_1=8$. Applying the condition: $2g(-3)+2f(0)=0+8$ $\Rightarrow -6g=8$ $\Rightarrow g=-\frac{4}{3}$.For the second circle $x^2+y^2-2x-2y-7=0$,we have $g_2=-1, f_2=-1, c_2=-7$. Applying the condition: $2g(-1)+2f(-1)=0-7 \Rightarrow -2g-2f=-7$.Substituting $g=-\frac{4}{3}$ into the second equation: $-2(-\frac{4}{3})-2f=-7$ $\Rightarrow \frac{8}{3}-2f=-7$ $\Rightarrow 2f = 7+\frac{8}{3} = \frac{29}{3}$ $\Rightarrow f=\frac{29}{6}$.The equation is $x^2+y^2+2(-\frac{4}{3})x+2(\frac{29}{6})y=0$.$x^2+y^2-\frac{8}{3}x+\frac{29}{3}y=0$.Multiplying by $3$,we get $3x^2+3y^2-8x+29y=0$.

The equation of the circle which passes through the origin and cuts orthogonally each of the circles $x^2+y^2-6x+8=0$ and $x^2+y^2-2x-2y-7=0$ is

Similar Questions

It is estimated that per minute each $cm^2$ of the Earth receives about $2 \ cal$ $(1 \ cal = 4.18 \ J)$ of heat energy from the Sun. This is called the Solar constant. In $SI$ units,the value is:

For $x \in \mathbb{R}$,the least value of $\frac{x^2-6x+5}{x^2+2x+1}$ is

Assertion : Yeasts such as $Saccharomyces \text{ } cerevisiae$ are used in baking industry.
Reason : Carbon dioxide produced during fermentation causes bread dough to rise by thermal expansion.

An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction:

What are $X$ and $Y$ in the following reaction sequence?
$C_2H_5OH$ $\xrightarrow{Cl_2} \underline{X}$ $\xrightarrow{Cl_2} \underline{Y}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module