What is ((x-20)^2)/4+((y+1)^2)/9 =1 ?

The solution to ((x-20)^2)/4+((y+1)^2)/9 =1 is Ellipse with (h,k)=(20,-1),a=2,b=3

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((x-20)^2)/4+((y+1)^2)/9 =1

\frac{( x - 20 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

(h, k) = (20, - 1), a = 2, b = 3

Solution steps

\frac{( x - 20 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

Rewrite

\frac{( x - 20 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - 20 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (20, - 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (20, - 1), b = 3, a = 2

\frac{( x + 1 ) ^{2}}{2} + \frac{( y - 6 ) ^{2}}{187} = 1

x^{2} + 5 y^{2} - 6 x + 20 y = - 24

\frac{( x - 1 ) ^{2}}{425} + \frac{( y - 2 ) ^{2}}{400} = 1

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

(\frac{x - 3}{2})^{2} + y^{2} = \frac{9}{4}

What is ((x-20)^2)/4+((y+1)^2)/9 =1 ?
The solution to ((x-20)^2)/4+((y+1)^2)/9 =1 is Ellipse with (h,k)=(20,-1),a=2,b=3