Question

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

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

Answer 1

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

Centre of circle = Point of intersection of diameters = (1, ­–1)

Now area = $154\Rightarrow \pi r^2=154\Rightarrow r=7$

Hence the equation of required circle is$(x-1{)}^2+(y+1{)}^2=7^2\Rightarrow x^2+y^2-2x+2y=47.$