The lines $2x-3y-5=0$ and $3x-4y=7$ are

diameters of a circle of area $154(=49\mathrm{\pi })$ sq. units, then the equation of

the circle is

The centre of the required circle lies at the

intersection of $2x-3y-5=0$ and $3x-4y-7=0.$ Thus, the

coordinates of the centre are (1, -1).

Let r be the radius of the circle. Then, by hypothesis, we have

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

Hence, the equation of the required circle is

$(x-1{)}^2+(y+1{)}^2=7^2\Rightarrow x^2+y^2-2x+2y-47=0$