What is 10x^2+3y^2=30 ?

The solution to 10x^2+3y^2=30 is Ellipse with (h,k)=(0,0),a=sqrt(3),b=sqrt(10)

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10x^2+3y^2=30

10 x^{2} + 3 y^{2} = 30

(h, k) = (0, 0), a = 3, b = 10

Solution steps

10 x^{2} + 3 y^{2} = 30

Rewrite

10 x^{2} + 3 y^{2} = 30

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 10, a = 3

\frac{x ^{2}}{k} + \frac{y ^{2}}{4 + k} = 1

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{( ( x - 4 ) ^{2} )}{36} + \frac{( ( y - 2 ) ^{2} )}{9} = 1

9 x^{2} + 16 y^{2} - 90 x - 160 y + 481 = 0

16 x^{2} + 49 y^{2} = 25

What is 10x^2+3y^2=30 ?
The solution to 10x^2+3y^2=30 is Ellipse with (h,k)=(0,0),a=sqrt(3),b=sqrt(10)