What is (x^2)/8+(y^2)/a =1 ?

The solution to (x^2)/8+(y^2)/a =1 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=sqrt(a)

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(x^2)/8+(y^2)/a =1

\frac{x ^{2}}{8} + \frac{y ^{2}}{a} = 1

(h, k) = (0, 0), a = 22, b = a

Solution steps

\frac{x ^{2}}{8} + \frac{y ^{2}}{a} = 1

Rewrite

\frac{x ^{2}}{8} + \frac{y ^{2}}{a} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 22, b = a

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

2 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

1 - x^{2} - y^{2} = 5

36 (x - \frac{1}{2})^{2} - \frac{1}{4} + 64 (y + 2)^{2} - 4 + 265 = 576

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{6 ^{2}} = 1

7 x^{2} + y^{2} = 8

What is (x^2)/8+(y^2)/a =1 ?
The solution to (x^2)/8+(y^2)/a =1 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=sqrt(a)