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

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

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9x^2+16y^2=4

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

(h, k) = (0, 0), a = \frac{2}{3}, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2}{3}, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{2}{3}, b = \frac{1}{2}

(x)^{2} + \frac{( y - 6 ) ^{2}}{12} = 1

\frac{x ^{2}}{3} + \frac{y ^{2}}{4} = 1

\frac{( X - 5 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

6 x^{2} + 10 x + y^{2} = 0

27 x^{2} - 54 x + 48 y^{2} - 192 y - 213 = 0

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