Q- two diameters of a circle are along the lines x-y-9=0 and x-2y-7=0 and area of the circle is 154 - Maths - Conic Sections

Question

Q- two diameters of a circle are along the lines x-y-9=0 and
x-2y-7=0 and area of the circle is 154 sq unit find the
equation

Rajat Sethi · Accepted Answer

Area of circle = 154⇒πr2=154⇒r2=49Now, equation of two diameters of the circle lies along the line x-y-9=0 and x-2y-7=0The point of intersection of diameters will give the centre of the circle
Solving   x-y-9=0 and x-2y-7=0,we getx=11 and y=2So, coordinate of centre = (11,2)=(x1,y1)Equation of circle:(x-x1)2+(y-y1)2=r2⇒(x-11)2+(y-2)2=49

Q- two diameters of a circle are along the lines x-y-9=0 and x-2y-7=0 and area of the circle is 154 sq. unit find the equation.