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

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

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

\frac{( x + 1 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{49} = 1

9 x^{2} + 4 y^{2} + 18 x - 8 y - 23 = 0

3 x^{2} + 4 y^{2} = 48

9 (x - 3)^{2} + 4 (y - 4)^{2} = 36

\frac{( x - 7 ) ^{2}}{3} + \frac{( y + 11 ) ^{2}}{5} = 1

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