What is (x^2)/9+(x^2}{16}+\frac{z^2)/9 =1 ?

The solution to (x^2)/9+(x^2}{16}+\frac{z^2)/9 =1 is Ellipse with (h,k)=(0,0),a= 12/5 ,b=3

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(x^2)/9+(x^2}{16}+\frac{z^2)/9 =1

\frac{x ^{2}}{9} + \frac{x ^{2}}{16} + \frac{z ^{2}}{9} = 1

(h, k) = (0, 0), a = \frac{12}{5}, b = 3

Solution steps

\frac{x ^{2}}{9} + \frac{x ^{2}}{16} + \frac{z ^{2}}{9} = 1

Rewrite

\frac{x ^{2}}{9} + \frac{x ^{2}}{16} + \frac{z ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{12}{5} ) ^{2}} + \frac{( z - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{12}{5}, 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 = \frac{12}{5}

9 x^{2} + 4 y^{2} - 72 x - 16 y + 124 = 0

8 x^{2} + 9 y^{2} + 24 x + 18 y = 10

x^{2} + y^{2} + 5 y = 0

1 x^{2} + 4 y^{2} + 10 x + 9 y - 10 = 0

x^{2} + \frac{( y - 6 ) ^{2}}{16} = 1

What is (x^2)/9+(x^2}{16}+\frac{z^2)/9 =1 ?
The solution to (x^2)/9+(x^2}{16}+\frac{z^2)/9 =1 is Ellipse with (h,k)=(0,0),a= 12/5 ,b=3