What is 36x^2+16y^2=576 ?

The solution to 36x^2+16y^2=576 is Ellipse with (h,k)=(0,0),a=4,b=6

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36x^2+16y^2=576

36 x^{2} + 16 y^{2} = 576

(h, k) = (0, 0), a = 4, b = 6

Solution steps

36 x^{2} + 16 y^{2} = 576

Rewrite

36 x^{2} + 16 y^{2} = 576

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 6, a = 4

9 x^{2} + 18 x + 16 y^{2} - 96 y + 9 = 0

3 x^{2} + 2 y^{2} \leq 13950

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

\frac{( x + 1 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

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

What is 36x^2+16y^2=576 ?
The solution to 36x^2+16y^2=576 is Ellipse with (h,k)=(0,0),a=4,b=6