What is 2x^2+3y^2=10 ?

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

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2x^2+3y^2=10

2 x^{2} + 3 y^{2} = 10

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

Solution steps

2 x^{2} + 3 y^{2} = 10

Rewrite

2 x^{2} + 3 y^{2} = 10

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

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

9 x^{2} + 16 y^{2} + 126 x + 96 y + 441 = 0

2 x^{2} + y^{2} - 10 = 0

3 x^{2} + 3 y^{2} + 12 y = 0

\frac{( x + 1 ) ^{2}}{22.33} + \frac{( y - 1 ) ^{2}}{16.75} = 1

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