What is 4y^2+9x^2=36 ?

The solution to 4y^2+9x^2=36 is Ellipse with (h,k)=(0,0),a=2,b=3

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4y^2+9x^2=36

4 y^{2} + 9 x^{2} = 36

(h, k) = (0, 0), a = 2, b = 3

Solution steps

4 y^{2} + 9 x^{2} = 36

Rewrite

4 y^{2} + 9 x^{2} = 36

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 3, a = 2

2 x^{2} + 3 y^{2} + 12 x = 10

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

\frac{( x + 3 ) ^{2}}{49} + \frac{( y - 5 ) ^{2}}{16} = 1

18 x^{2} - 72 x + 4 y^{2} + 4 y + 37 = 0

6 (x + 1)^{2} + 2 (y - 1)^{2} = 72

What is 4y^2+9x^2=36 ?
The solution to 4y^2+9x^2=36 is Ellipse with (h,k)=(0,0),a=2,b=3