Someone tell me if this equation is a circle or parabola

Question

anonymous · Answer

4x^2+4y^2-16y+15=0

anonymous · Answer

Circle mate

anonymous · Answer

i think it can be an ellipse as well.

kainui · Answer

@the11stalker It's a circle because the x^2 and y^2 terms both have the same coefficient.

anonymous · Answer

oh yeah i didnt see that my mistake at fisrt glance looked to me like an ellipse

anonymous · Answer

This equation is known as a conic section. In this equation, we do happen to have a circle. Just so you know the difference in the standard equations of the conic sections (parabola and circle)$$x^2 + y^2 + Dx + Ey + F = 0$$ is the standard equation of a Circle. Like they've been saying, a circle's coefficients in front of x^2 and y^2 must be the same. 
$$y = a(x – h)^2 + k $$ this is the equation for a parabola that opens up or down.
$$x = a(y – k)^2 + h $$ this is the equation for a parabola that opens sideways (left or right).
I'm in Honors Advanced Algebra (A combo of Algebra 2 and Algebra 3, and these formulas are the ones used internationally and on big standardized tests like EOC Tests, State Tests, SAT, PSAT, and the ACT.) Hope this helped!

anonymous · Answer

Guys, It's a circle..........

rock_mit182 · Answer

mm darn it of course ! just that no have translation in x