What is 20x^2+9y^2=225 ?

The solution to 20x^2+9y^2=225 is Ellipse with (h,k)=(0,0),a=(3sqrt(5))/2 ,b=5

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20x^2+9y^2=225

20 x^{2} + 9 y^{2} = 225

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

Solution steps

20 x^{2} + 9 y^{2} = 225

Rewrite

20 x^{2} + 9 y^{2} = 225

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

x^{(2)} + 4 y^{(2)} - 10 x - 40 y + 109 y = 0

x^{2} - 6 y + y^{2} = 0

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

\frac{( ( x + 5 ) ^{2} )}{10} + \frac{( ( y + 4 ) ^{2} )}{8} = 1

3 x^{2} + y^{2} = 25

What is 20x^2+9y^2=225 ?
The solution to 20x^2+9y^2=225 is Ellipse with (h,k)=(0,0),a=(3sqrt(5))/2 ,b=5