What is (y^2}{16}=1-\frac{x^2)/9 ?

The solution to (y^2}{16}=1-\frac{x^2)/9 is Ellipse with (h,k)=(0,0),a=3,b=4

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(y^2}{16}=1-\frac{x^2)/9

\frac{y ^{2}}{16} = 1 - \frac{x ^{2}}{9}

(h, k) = (0, 0), a = 3, b = 4

Solution steps

\frac{y ^{2}}{16} = 1 - \frac{x ^{2}}{9}

Rewrite

\frac{y ^{2}}{16} = 1 - \frac{x ^{2}}{9}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = 3

4 x^{2} + 9 y^{2} + 16 x - 36 y + 16 = 0

- 16 - x^{2} - y^{2} \geq 0

9 = 4 x^{2} + y^{2}

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{36} = 1

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

What is (y^2}{16}=1-\frac{x^2)/9 ?
The solution to (y^2}{16}=1-\frac{x^2)/9 is Ellipse with (h,k)=(0,0),a=3,b=4