if the equation ax^2 + (2-b)xy + 3y^2 - 6bx + 30y + 6b = 0 is circle then find - Maths - Conic Sections

Question

if the equation ax^2 + (2-b)xy + 3y^2 - 6bx + 30y + 6b = 0 is
circle then find a^2 + b^2 = ?

Vivek Rai · Accepted Answer

Dear student
ax2+(2-b)xy+3y2-6bx+30y+6b=0 has to represent circle,then 2-b=0, and a=3,⇒b=2,a=3*as for a 2o equation, ax2+by2+2hxy+2gx+2fy+c=0, we must have a=b, and h=0As by applying these 2 conditions, we got a=3,b=2⇒a2+b2=9+4=13
Hope this clears your doubt
With regards

if the equation ax^2 + (2-b)xy + 3y^2 - 6bx + 30y + 6b = 0 is circle then find a^2 + b^2 = ?