What is (x^2)/5+(y^2)/3 =1 ?

The solution to (x^2)/5+(y^2)/3 =1 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=sqrt(3)

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(x^2)/5+(y^2)/3 =1

\frac{x ^{2}}{5} + \frac{y ^{2}}{3} = 1

(h, k) = (0, 0), a = 5, b = 3

Solution steps

\frac{x ^{2}}{5} + \frac{y ^{2}}{3} = 1

Rewrite

\frac{x ^{2}}{5} + \frac{y ^{2}}{3} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 5, b = 3

16 x^{2} + 25 y^{2} - 64 x + 150 y - 11 = 0

\frac{( x + 3 ) ^{2}}{49} + \frac{y ^{2}}{36} = 1

25 x^{2} + 16 y^{2} - 350 x + 96 y - 231 = 0

4 x^{2} + 3 y^{2} - 12 = 0

x^{2} + y^{2} = 6 y

What is (x^2)/5+(y^2)/3 =1 ?
The solution to (x^2)/5+(y^2)/3 =1 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=sqrt(3)