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

The solution to 9z^2+y^2=36 is Ellipse with (h,k)=(0,0),a=2,b=6

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9z^2+y^2=36

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

(h, k) = (0, 0), a = 2, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

\frac{( x - 3 ) ^{2}}{12} + \frac{y ^{2}}{16} = 1

4 a^{2} + 9 b^{2} = 25

3 x^{2} + 3 y^{2} + 48 y = 0

25 x^{(2)} + 4 y^{(2)} = 99

3 x^{2} - 9 x + 2 y^{2} + 10 y - 6 = 0

What is 9z^2+y^2=36 ?
The solution to 9z^2+y^2=36 is Ellipse with (h,k)=(0,0),a=2,b=6