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

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

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

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

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

Solution steps

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

Rewrite

x^{2} - 6 x + 4 y^{2} + 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

\frac{( x + 3 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{25} = 1

16 x^{2} + 36 y^{2} - 96 x + 36 y + 9 = 0

\frac{x ^{2}}{144} + \frac{y ^{2}}{16} = 1

(2 x - 2)^{2} + (3 y - 6)^{2} = 36

\frac{x ^{2}}{12} + \frac{y ^{2}}{16} = 1

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