What is 4x^2+y^2+6y+5=0 ?

The solution to 4x^2+y^2+6y+5=0 is Ellipse with (h,k)=(0,-3),a=1,b=2

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4x^2+y^2+6y+5=0

4 x^{2} + y^{2} + 6 y + 5 = 0

(h, k) = (0, - 3), a = 1, b = 2

Solution steps

4 x^{2} + y^{2} + 6 y + 5 = 0

Rewrite

4 x^{2} + y^{2} + 6 y + 5 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 1, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), b = 2, a = 1

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

9 x^{2} - 18 x + 4 y^{2} + 16 y - 11 = 0

3 x^{2} + 5 y^{2} - 6 = 0

16 x^{2} + 25 y^{2} - 48 x + 100 y - 264 = 0

x^{2} + 4 x + 4 y^{2} - 8 y + 4 = 0

What is 4x^2+y^2+6y+5=0 ?
The solution to 4x^2+y^2+6y+5=0 is Ellipse with (h,k)=(0,-3),a=1,b=2