What is (x^2)/(5^2)+(y^2)/(13^2)=1 ?

The solution to (x^2)/(5^2)+(y^2)/(13^2)=1 is Ellipse with (h,k)=(0,0),a=5,b=13

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(x^2)/(5^2)+(y^2)/(13^2)=1

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

(h, k) = (0, 0), a = 5, b = 13

Solution steps

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

Rewrite

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{1 3 ^{2}} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 13

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 13, a = 5

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

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

\frac{( x + 3 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{4} = 1

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

x^{2} + (8 - 6) y^{2} = 1

What is (x^2)/(5^2)+(y^2)/(13^2)=1 ?
The solution to (x^2)/(5^2)+(y^2)/(13^2)=1 is Ellipse with (h,k)=(0,0),a=5,b=13