What is (x^2-4)/(6^2)+(y^2+4)/(2^2)=1 ?

The solution to (x^2-4)/(6^2)+(y^2+4)/(2^2)=1 is Ellipse with (h,k)=(0,0),a=2,b= 2/3

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(x^2-4)/(6^2)+(y^2+4)/(2^2)=1

\frac{x ^{2} - 4}{6 ^{2}} + \frac{y ^{2} + 4}{2 ^{2}} = 1

(h, k) = (0, 0), a = 2, b = \frac{2}{3}

Solution steps

\frac{x ^{2} - 4}{6 ^{2}} + \frac{y ^{2} + 4}{2 ^{2}} = 1

Rewrite

\frac{x ^{2} - 4}{6 ^{2}} + \frac{y ^{2} + 4}{2 ^{2}} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = \frac{2}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 2, b = \frac{2}{3}

What is (x^2-4)/(6^2)+(y^2+4)/(2^2)=1 ?
The solution to (x^2-4)/(6^2)+(y^2+4)/(2^2)=1 is Ellipse with (h,k)=(0,0),a=2,b= 2/3