What is -2x^2-8x-y^2+16y=52 ?

The solution to -2x^2-8x-y^2+16y=52 is Ellipse with (h,k)=(-2,8),a=sqrt(10),b=2sqrt(5)

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-2x^2-8x-y^2+16y=52

- 2 x^{2} - 8 x - y^{2} + 16 y = 52

(h, k) = (- 2, 8), a = 10, b = 25

Solution steps

- 2 x^{2} - 8 x - y^{2} + 16 y = 52

Rewrite

- 2 x^{2} - 8 x - y^{2} + 16 y = 52

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 8 ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 8), a = 10, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 8), b = 25, a = 10

9 x^{2} + 4 y^{2} - 90 x + 32 y + 145 = 0

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 6 ) ^{2}}{16} = 1

\frac{( x + 3 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

4 x^{2} - 48 x + 9 y^{2} + 72 y + 144 = 0

\frac{( x - 2.22 ) ^{2}}{2.54} + \frac{y ^{2}}{1.11} = 2

What is -2x^2-8x-y^2+16y=52 ?
The solution to -2x^2-8x-y^2+16y=52 is Ellipse with (h,k)=(-2,8),a=sqrt(10),b=2sqrt(5)