What is (-y-6)^2+8x^2=64 ?

The solution to (-y-6)^2+8x^2=64 is Ellipse with (h,k)=(0,-6),a=2sqrt(2),b=8

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(-y-6)^2+8x^2=64

(- y - 6)^{2} + 8 x^{2} = 64

(h, k) = (0, - 6), a = 22, b = 8

Solution steps

(- y - 6)^{2} + 8 x^{2} = 64

Rewrite

(- y - 6)^{2} + 8 x^{2} = 64

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 2 ) ^{2}} + \frac{( y - ( - 6 ) ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 6), a = 22, b = 8

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 6), b = 8, a = 22

4 x^{2} + 24 x + 25 y^{2} + 200 y + 336 = 0

3 (x + 1)^{2} + (y - 1)^{2} = 6

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} = 0

7 x^{2} + 16 y^{2} - 14 x - 64 y - 41 = 0

0 = \frac{1}{2} x^{2} - 1 + \frac{1}{4} y^{2}

What is (-y-6)^2+8x^2=64 ?
The solution to (-y-6)^2+8x^2=64 is Ellipse with (h,k)=(0,-6),a=2sqrt(2),b=8