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

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

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

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

(h, k) = (0, 0), a = 3, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = 2

\frac{( x - 2 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{25} = 1

3 x^{2} + 4 y^{2} - 16 x + 16 = 0

x^{2} + 2 y^{2} + 4 x + 2 y - 27 = 0

(6 (x)^{2} - 12 x) + ((y)^{2} + 4 y) = - 4

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