What is 20x^2+36y^2=405 ?

The solution to 20x^2+36y^2=405 is Ellipse with (h,k)=(0,0),a= 9/2 ,b=(3sqrt(5))/2

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20x^2+36y^2=405

20 x^{2} + 36 y^{2} = 405

(h, k) = (0, 0), a = \frac{9}{2}, b = \frac{3 5}{2}

Solution steps

20 x^{2} + 36 y^{2} = 405

Rewrite

20 x^{2} + 36 y^{2} = 405

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{9}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{3 5}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{9}{2}, b = \frac{3 5}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{9}{2}, b = \frac{3 5}{2}

\frac{x}{x ^{2} + y ^{2}} = \frac{3}{4}

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

\frac{( ( x - 2 ) ^{2} )}{4} + \frac{( ( y + 4 ) ^{2} )}{16} = 1

36 X^{2} + 25 Y^{2} = 900

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{4 ^{2}} = 1

What is 20x^2+36y^2=405 ?
The solution to 20x^2+36y^2=405 is Ellipse with (h,k)=(0,0),a= 9/2 ,b=(3sqrt(5))/2