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

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

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4y^2+9z^2=36

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

3 (3 x^{2} + 9 y^{2} - 2 x - 36) = - 82

h (x) h (x) = - 5 x^{2} + 10 x + 15

9 x^{2} + y^{2} - 81 = 0

\frac{x ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

16 x^{2} + 80 y^{2} = 1280

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