What is 9x^2+4y^2=16 ?

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

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9x^2+4y^2=16

9 x^{2} + 4 y^{2} = 16

(h, k) = (0, 0), a = \frac{4}{3}, b = 2

Solution steps

9 x^{2} + 4 y^{2} = 16

Rewrite

9 x^{2} + 4 y^{2} = 16

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{4}{3}, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = \frac{4}{3}

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

36 - 4 x^{2} - 9 y^{2} > 0

\frac{x ^{2}}{64} + \frac{y ^{2}}{49} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{100} = 1

4 x^{2} + 16 y^{2} - 8 x - 96 y + 84 = 0

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