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

The solution to x^2+4y^2-6x+16y=0 is Ellipse with (h,k)=(3,-2),a=5,b= 5/2

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

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

(h, k) = (3, - 2), a = 5, b = \frac{5}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 2), a = 5, b = \frac{5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 2), a = 5, b = \frac{5}{2}

2 x^{2} + 4 y^{2} + 10 x + 10 y - 3 = 0

9 x^{2} + 25 y^{2} - 18 x + 200 y + 184 = 0

(x^{2} + 9 x) + (4 y^{2} + 10) = 5

\frac{( x - 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{( x - 9 ) ^{2}}{16} + \frac{( y - 11 ) ^{2}}{9} = 1

What is x^2+4y^2-6x+16y=0 ?
The solution to x^2+4y^2-6x+16y=0 is Ellipse with (h,k)=(3,-2),a=5,b= 5/2