What is 2x^2+3(y-2)^2=20 ?

The solution to 2x^2+3(y-2)^2=20 is Ellipse with (h,k)=(0,2),a=sqrt(10),b=(2sqrt(5))/(sqrt(3))

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2x^2+3(y-2)^2=20

2 x^{2} + 3 (y - 2)^{2} = 20

(h, k) = (0, 2), a = 10, b = \frac{2 5}{3}

Solution steps

2 x^{2} + 3 (y - 2)^{2} = 20

Rewrite

2 x^{2} + 3 (y - 2)^{2} = 20

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( \frac{2 5}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 10, b = \frac{2 5}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 10, b = \frac{2 5}{3}

2 x^{2} + 8 x + y^{2} - 3 y = 0

\frac{x ^{2}}{179} + \frac{y ^{2}}{120} = 1

2 x^{2} + y^{2} = 57

\frac{( x - 3 ) ^{2}}{49} + \frac{( y - 5 ) ^{2}}{4} = 1

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

What is 2x^2+3(y-2)^2=20 ?
The solution to 2x^2+3(y-2)^2=20 is Ellipse with (h,k)=(0,2),a=sqrt(10),b=(2sqrt(5))/(sqrt(3))