What is (x^2)/9+(y^2)/(20)=1 ?

The solution to (x^2)/9+(y^2)/(20)=1 is Ellipse with (h,k)=(0,0),a=3,b=2sqrt(5)

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(x^2)/9+(y^2)/(20)=1

\frac{x ^{2}}{9} + \frac{y ^{2}}{20} = 1

(h, k) = (0, 0), a = 3, b = 25

Solution steps

\frac{x ^{2}}{9} + \frac{y ^{2}}{20} = 1

Rewrite

\frac{x ^{2}}{9} + \frac{y ^{2}}{20} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 25, a = 3

\frac{x ^{2} + y ^{2} + 8 y - 16}{x ^{2} + y ^{2} + 8 y + 16} = 9

5 x^{2} - 30 x + 9 y^{2} - 3 y + 36 = 0

2 x^{2} - 9 x + 4 y^{2} + 8 x = 16

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

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

What is (x^2)/9+(y^2)/(20)=1 ?
The solution to (x^2)/9+(y^2)/(20)=1 is Ellipse with (h,k)=(0,0),a=3,b=2sqrt(5)