What is (x^2)/(12^2)+(y^2)/(5^2)=1 ?

The solution to (x^2)/(12^2)+(y^2)/(5^2)=1 is Ellipse with (h,k)=(0,0),a=12,b=5

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(x^2)/(12^2)+(y^2)/(5^2)=1

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

(h, k) = (0, 0), a = 12, b = 5

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 12, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 12, b = 5

36 x^{2} + 16 y^{2} - 576 = 0

\frac{x ^{2}}{9} + \frac{2 x}{3} + 16 y^{2} - 64 y + \frac{569}{9} = 0

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

\frac{( ( x + 0 ) ^{2} )}{20} + \frac{( ( y + 0 ) ^{2} )}{16} = 1

x^{2} + 4 y^{2} - 4 x - 8 y = 0

What is (x^2)/(12^2)+(y^2)/(5^2)=1 ?
The solution to (x^2)/(12^2)+(y^2)/(5^2)=1 is Ellipse with (h,k)=(0,0),a=12,b=5