What is 5x^2+z^2=100 ?

The solution to 5x^2+z^2=100 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=10

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5x^2+z^2=100

5 x^{2} + z^{2} = 100

(h, k) = (0, 0), a = 25, b = 10

Solution steps

5 x^{2} + z^{2} = 100

Rewrite

5 x^{2} + z^{2} = 100

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 25, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 10, a = 25

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{36} = 1

\frac{25 x ^{2}}{400 - 1 2 ^{2}} + \frac{16 y ^{2}}{400 - 1 2 ^{2}} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{225} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{169} + \frac{( y + 4 ) ^{2}}{144} = 1

What is 5x^2+z^2=100 ?
The solution to 5x^2+z^2=100 is Ellipse with (h,k)=(0,0),a=2sqrt(5),b=10