if3x^2+axy+by^2+6x+12y-5=0 represents a circle . find a,b find its center
Answers
value of a = 0 and b = 3
we know, standard equation of circle is x² + y² + 2gx + 2fy + c = 0,
means, for circle
coefficient of x² = coefficient of y²
coefficient of xy = 0
so, given equation , 3x² + axy + by² + 6x + 12xy - 5 = 0 will be circle when ,
a = 0 and b = 3
[note : conic section standard equation is ax² + by² + 2hxy + 2gx + 2fy + c = 0. for circle , ∆ = abc + 2fgh - af² - bg² - ch² ≠ 0. you can check by putting, a =0 and b = 3. definitely you will get ∆ ≠ 0. ]
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