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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

25 x^{2} + 16 y^{2} + 200 x - 160 y + 400 = 0

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

4 x^{2} + 9 y^{2} - 48 x + 72 y = - 144

4 - x^{2} - 4 y^{2} \geq 0

\frac{( x + 5 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{36} = 1

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