What is 4x^2+z^2=16 ?

The solution to 4x^2+z^2=16 is Ellipse with (h,k)=(0,0),a=2,b=4

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4x^2+z^2=16

4 x^{2} + z^{2} = 16

(h, k) = (0, 0), a = 2, b = 4

Solution steps

4 x^{2} + z^{2} = 16

Rewrite

4 x^{2} + z^{2} = 16

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = 2

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{36} = 1

100 x^{2} + 64 y^{2} - 100 x - 1575 = 0

x^{2} + \frac{y ^{2}}{29} = 1

100 (x^{2} - x) + 16 (y^{2} - 4 y) = 147

14 x^{2} + 9 y^{2} = 126

What is 4x^2+z^2=16 ?
The solution to 4x^2+z^2=16 is Ellipse with (h,k)=(0,0),a=2,b=4