Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Diameter of give circles

2x-3y+12=0 .............(1)

x+4y-5=0 .............(2)

Intersection point of these two diameter will give us the centre of circle.

solving equation 1 & 2.

multiply 2 in equation (2) and substarct it from equation (1)

x=-3,y=2

Center of the circle (-3,2)

Given area of circle =154

$\pi r^2=154$

$\frac{22}{7}\times r^2=154$

r=7

The director circle of a circle is the concentric circle having radius equal to $\sqrt{2}$ times the original circle

center of director circle (-3,2)

Radius of director circle $=\sqrt{2}\times 7$

$(x+3{)}^2+(y-2{)}^2=(\sqrt{2}\times 7{)}^2$

$(x+3{)}^2+(y-2{)}^2=98$

$x^2+9+6x+y^2+4-4y=98$

$x^2+y^2+6x-4y-85=0$

Option D is correct