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

The solution to (y^2}{16}+\frac{z^2)/9 =1 is Ellipse with (h,k)=(0,0),a=4,b=3

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

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

(h, k) = (0, 0), a = 4, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( y - 0 ) ^{2}}{4 ^{2}} + \frac{( z - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = 3

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

\frac{x ^{2}}{169} + \frac{y ^{2}}{36} = 1

3 y^{2} + x^{2} - 12 y + 9 = 0

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

16 x^{2} + 4 y^{2} + 16 x + 49 y - 81 = 0

What is (y^2}{16}+\frac{z^2)/9 =1 ?
The solution to (y^2}{16}+\frac{z^2)/9 =1 is Ellipse with (h,k)=(0,0),a=4,b=3