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

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

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

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

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

Solution steps

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

Rewrite

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

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

10 x^{2} + 4 y^{2} = 14

\frac{( x + 6 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{16} = 1

2 x^{2} - 5 x + 3 y^{2} - 4 y = 1

5 x^{2} + 10 y^{2} = 5

3 x^{2} + 3 y^{2} + 36 y = 0

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