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

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

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y^2=1-(x^2)/(a^2)

y^{2} = 1 - \frac{x ^{2}}{a ^{2}}

(h, k) = (0, 0), a = a, b = 1

Solution steps

y^{2} = 1 - \frac{x ^{2}}{a ^{2}}

Rewrite

y^{2} = 1 - \frac{x ^{2}}{a ^{2}}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = a, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = a, b = 1

25 x^{2} + 9 y^{2} + 200 x - 36 y + 211 = 0

4 x^{2} + 9 y^{2} - 8 x + 36 y + 4 = 0

- 5 x^{2} - 6 y^{2} = 1

\frac{( x + 2 ) ^{2}}{( - 13 ) ^{2}} + \frac{( y - 3 ) ^{2}}{( - 8 ) ^{2}} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 25

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