What is 16-x^2-9y^2=0 ?

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

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16-x^2-9y^2=0

16 - x^{2} - 9 y^{2} = 0

(h, k) = (0, 0), a = 4, b = \frac{4}{3}

Solution steps

16 - x^{2} - 9 y^{2} = 0

Rewrite

16 - x^{2} - 9 y^{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = \frac{4}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = \frac{4}{3}

256 x^{2} - 800 x + 625 = 400 x^{2} - 800 x + 400 y^{2} + 400

- 2 = \frac{2 x}{x ^{2} + y ^{2}}

16 - x^{2} - 9 y^{2} > 0

9 x^{2} + 7 y^{2} = 1

8 x^{2} - 96 x + 18 y^{2} + 144 y + 288 = 0

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