What is 4x^2+y^2+2y-15=0 ?

The solution to 4x^2+y^2+2y-15=0 is Ellipse with (h,k)=(0,-1),a=2,b=4

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

4 x^{2} + y^{2} + 2 y - 15 = 0

(h, k) = (0, - 1), a = 2, b = 4

Solution steps

4 x^{2} + y^{2} + 2 y - 15 = 0

Rewrite

4 x^{2} + y^{2} + 2 y - 15 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 1), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 4, a = 2

9 x^{2} + 49 y^{2} + 18 x + 294 y - 9 = 0

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

3 = x^{2} + 4 y^{2}

\frac{X ^{2}}{4} + \frac{Y ^{2}}{9} = 4

\frac{x ^{2}}{2.4 8 ^{2}} + \frac{y ^{2}}{2.7 5 ^{2}} = 1

What is 4x^2+y^2+2y-15=0 ?
The solution to 4x^2+y^2+2y-15=0 is Ellipse with (h,k)=(0,-1),a=2,b=4