What is (x^2)/(6^2)+(y^2)/(3^2)=1 ?

The solution to (x^2)/(6^2)+(y^2)/(3^2)=1 is Ellipse with (h,k)=(0,0),a=6,b=3

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(x^2)/(6^2)+(y^2)/(3^2)=1

\frac{x ^{2}}{6 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

(h, k) = (0, 0), a = 6, b = 3

Solution steps

\frac{x ^{2}}{6 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

Rewrite

\frac{x ^{2}}{6 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = 3

\frac{( x + 5 ) ^{2}}{4} + \frac{( y - 1 ) ^{2}}{25} = 1

25 x^{2} + 36 y^{2} - 350 x + 350 = 0

4 (x - 4)^{2} + 9 (y + 5)^{2} = 36

15 x^{2} + 15 y^{2} + 16 y \geq 0

\frac{( y - 3 ) ^{2}}{64} + \frac{( x + 5 ) ^{2}}{81} = 1

What is (x^2)/(6^2)+(y^2)/(3^2)=1 ?
The solution to (x^2)/(6^2)+(y^2)/(3^2)=1 is Ellipse with (h,k)=(0,0),a=6,b=3