What is (x^2)/(3^2)+(y^2)/(4^2)=1 ?

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

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(x^2)/(3^2)+(y^2)/(4^2)=1

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

(h, k) = (0, 0), a = 3, b = 4

Solution steps

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

Rewrite

\frac{x ^{2}}{3 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = 3

2 = \frac{x ^{2}}{4} + \frac{y ^{2}}{9}

\frac{( x + 4 ) ^{2}}{9} + \frac{( y + 4 ) ^{2}}{4} = 1

3 x^{2} + 2 y^{2} + 2 x - 3 y - 7 = 0

x^{2} + 2 x + 4 y^{2} - 8 y + 1 = 0

25 x^{2} + 4 y^{2} - 8 y - 50 x = 71

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