Question

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

• A. $x^2+y^2-2x-2y=47$
• B. $x^2+y^2-2x-2y=62$
• C. $x^2+y^2-2x+2y=47$
• D. $x^2+y^2-2x+2y=62$

Answer 1

The correct option is C $x^2+y^2-2x+2y=47$

The centre of circle is the point of intersection of the given diameter $2x-3y=5$ and $3x-4y=7$
which is $(1,-1)$ and if r is the radius of the circle ,then
$\pi r^2=154\Rightarrow r^2=154\times \frac{7}{22}\Rightarrow r=7$
Hence an equation of the required circle is
${(x-1)}^2+{(y+1)}^2=7^2\Rightarrow x^2+y^2-2x+2y=47$