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

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

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

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

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

Solution steps

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

Rewrite

\frac{y ^{2}}{b ^{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}}{b ^{2}} = 1

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

- 1 (- 4 x^{2} - y^{2} + 16) \geq - 1 (0)

\frac{x ^{2}}{14} + \frac{y ^{2}}{8} = 1

- 1.14 y^{2} = 52.3 + x^{2}

\frac{( x - 3 ) ^{2}}{\frac{2}{9}} + \frac{( y - 5 ) ^{2}}{25} = 1

5 x^{2} - 70 x + 9 y^{2} + 90 y + 425 = 0

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