What is 3y^2+5x^2=20 ?

The solution to 3y^2+5x^2=20 is Ellipse with (h,k)=(0,0),a=2,b=(2sqrt(5))/(sqrt(3))

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3y^2+5x^2=20

3 y^{2} + 5 x^{2} = 20

(h, k) = (0, 0), a = 2, b = \frac{2 5}{3}

Solution steps

3 y^{2} + 5 x^{2} = 20

Rewrite

3 y^{2} + 5 x^{2} = 20

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = \frac{2 5}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{2 5}{3}, a = 2

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{20} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{8} = 1

4 x^{2} + 9 y^{2} + 24 x = 0

\frac{x ^{2}}{81} + \frac{y ^{2}}{25} = 1

\frac{x ^{2} - 2 x + y ^{2}}{4 - y} < 14

What is 3y^2+5x^2=20 ?
The solution to 3y^2+5x^2=20 is Ellipse with (h,k)=(0,0),a=2,b=(2sqrt(5))/(sqrt(3))