SOLUTION: What shape does this equation make? (circle, ellipse, hyperbola) 4x^2 + 16x + y^2

SOLUTION: What shape does this equation make? (circle, ellipse, hyperbola) 4x^2 + 16x + y^2 - 6y = -21

Question 194051: What shape does this equation make? (circle, ellipse, hyperbola)
4x^2 + 16x + y^2 - 6y = -21
Found 2 solutions by solver91311, RAY100:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Both the and term coefficients have the same sign, so it is either a circle or an ellipse. But the coefficients on the and terms are unequal, so it is an ellipse.

In summary:

Equal coefficients on and means circle.

Unequal coefficients, but the same sign means ellipse.

Opposite signs on the coefficients means hyperbola.

Zero coefficient on either the and terms (but NOT both) means parabola.

John

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
4x^2 + 16x +y^2 -6y = -21
,
if we complete the squares, we can see form
,
4 (x^2 +4x +4) +y^2 -6y +9 = -21 +16 +9,,,,(4*4=16)
,,,,
remember (4/2)^2 = 4 and (-6/2)^2 =9,,,, and add to both sides to balance
,
4(x+2)^2 + (y-3)^2 = 4
,
divide thru by 4
,
((x+2)^2)/1 +( (y-3)^2 )/4=4/4=1
,
the form for ellipse is, x^2/a^2 +y^2/b^2 =1
therefore it fits an ellipse
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