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

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

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5x^2+3y^2=15

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

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

Solution steps

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

Rewrite

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

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

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{4} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{( 4 - 16 )} = 1

9 x^{2} + y^{2} - 100 = 0

9 x^{2} + 16 y^{2} + 180 x - 256 y - 452 = 0

9 x^{2} + 6 y^{2} = 54

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