What is (x^2)/(10^2)+(y^2)/(5^2)=1 ?

The solution to (x^2)/(10^2)+(y^2)/(5^2)=1 is Ellipse with (h,k)=(0,0),a=10,b=5

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(x^2)/(10^2)+(y^2)/(5^2)=1

\frac{x ^{2}}{1 0 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

(h, k) = (0, 0), a = 10, b = 5

Solution steps

\frac{x ^{2}}{1 0 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

Rewrite

\frac{x ^{2}}{1 0 ^{2}} + \frac{y ^{2}}{5 ^{2}} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = 5

5 x^{2} + 20 x + 7 y^{2} + 14 y = 8

(\frac{x ^{2}}{4}) + \frac{y ^{2}}{9} = 5

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

25 x^{2} + (y^{2} - 4 y) = 21

\frac{x ^{2}}{25} - 13 y + 17 x = - \frac{y ^{2}}{49} + 1

What is (x^2)/(10^2)+(y^2)/(5^2)=1 ?
The solution to (x^2)/(10^2)+(y^2)/(5^2)=1 is Ellipse with (h,k)=(0,0),a=10,b=5