What is x^2+4y^2-6x+16y=-9 ?

The solution to x^2+4y^2-6x+16y=-9 is Ellipse with (h,k)=(3,-2),a=4,b=2

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x^2+4y^2-6x+16y=-9

x^{2} + 4 y^{2} - 6 x + 16 y = - 9

(h, k) = (3, - 2), a = 4, b = 2

Solution steps

x^{2} + 4 y^{2} - 6 x + 16 y = - 9

Rewrite

x^{2} + 4 y^{2} - 6 x + 16 y = - 9

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), a = 4, b = 2

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

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

What is x^2+4y^2-6x+16y=-9 ?
The solution to x^2+4y^2-6x+16y=-9 is Ellipse with (h,k)=(3,-2),a=4,b=2