What is 20(x+1)^2+9y^2=180 ?

The solution to 20(x+1)^2+9y^2=180 is Ellipse with (h,k)=(-1,0),a=3,b=2sqrt(5)

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20(x+1)^2+9y^2=180

20 (x + 1)^{2} + 9 y^{2} = 180

(h, k) = (- 1, 0), a = 3, b = 25

Solution steps

20 (x + 1)^{2} + 9 y^{2} = 180

Rewrite

20 (x + 1)^{2} + 9 y^{2} = 180

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 3, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), b = 25, a = 3

x^{2} + 5 y^{2} = \frac{1}{5}

3 x^{2} + 12 y^{2} + 18 x - 24 y - 69 = 0

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

3 y^{2} + 5 x^{2} = 20

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{20} = 1

What is 20(x+1)^2+9y^2=180 ?
The solution to 20(x+1)^2+9y^2=180 is Ellipse with (h,k)=(-1,0),a=3,b=2sqrt(5)