What is x^2+4y^2+6x+16y+21=0 ?

The solution to x^2+4y^2+6x+16y+21=0 is Ellipse with (h,k)=(-3,-2),a=2,b=1

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x^2+4y^2+6x+16y+21=0

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

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

Solution steps

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

Rewrite

x^{2} + 4 y^{2} + 6 x + 16 y + 21 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

y^{2} = 12 x

\frac{y ^{2}}{16} - \frac{x ^{2}}{9} = 1

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

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{25} - \frac{y ^{2}}{9} = 1

What is x^2+4y^2+6x+16y+21=0 ?
The solution to x^2+4y^2+6x+16y+21=0 is Ellipse with (h,k)=(-3,-2),a=2,b=1