Question

The equation of director circle of the circle two of whose diameter are $2x-3y+12=0$ and $x+4y-5=0$ and area is $154$ square units .

• A. ${(x-3)}^2+{(y-2)}^2=98$
• B. ${(x-3)}^2+{(y+2)}^2=98$
• C. ${(x+3)}^2+{(y+2)}^2=98$
• D. ${(x+3)}^2+{(y-2)}^2=98$

Answer 1

The correct option is C ${(x+3)}^2+{(y+2)}^2=98$

Solving the equation of diameters of the given circle we get the centre as $(-3,-2)$.
$\pi r^2=154\frac{22}{7}{r}^2=154\Rightarrow r^2=49\Rightarrow r=7$
Director circle is the concentric of radius $\sqrt{2}$ times the radius of given circle
So radius of director circle $=7\sqrt{2}$
Equation of director circle is
${(x+3)}^2+{(y+2)}^2={\left(7\sqrt{2}\right)}^2{(x+3)}^2+{(y+2)}^2=98$