What is 3x^2+5y^2=15 ?

The solution to 3x^2+5y^2=15 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=sqrt(3)

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3x^2+5y^2=15

3 x^{2} + 5 y^{2} = 15

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

Solution steps

3 x^{2} + 5 y^{2} = 15

Rewrite

3 x^{2} + 5 y^{2} = 15

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

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

8 x^{2} + 9 y^{2} - 16 x - 18 y - 55 = 0

\frac{x ^{2}}{576} + \frac{y ^{2}}{676} = 1

9 x^{2} + y^{2} - 18 x - 6 y + 9 = 0

25 x^{2} + 10 y^{2} = 50

What is 3x^2+5y^2=15 ?
The solution to 3x^2+5y^2=15 is Ellipse with (h,k)=(0,0),a=sqrt(5),b=sqrt(3)