The lines 2x-3y=5 and 3x-4y=7 are diameters of a circle having area 154 sq.

Question

The lines $2x-3y=5$ and $3x-4y=7$ are diameters of a circle having area $154$ sq. units. Then the equation of the circle is:

Accepted Answer

$$\pi {r^2} = 154 \Rightarrow r = 7$$

For center on solving equation

$$2x - 3y = 5\& 3x - 4y = 7$$

we get $$x = 1,\,y =  - 1$$

$$\therefore$$ center $=(1,-1)$

Equation of circle,

$${\left( {x - 1} \right)^2} + {\left( {y + 1} \right)^2} = {7^2}$$

${x^2} + {y^2} - 2x + 2y = 47$

Solutions · 1