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

The solution to ((x+2)^2)/4+((y-4)^2)/(20)=1 is Ellipse with (h,k)=(-2,4),a=2,b=2sqrt(5)

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

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

(h, k) = (- 2, 4), a = 2, b = 25

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 4), a = 2, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 4), b = 25, a = 2

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

x^{2} + y^{2} = - y^{2} + 4

(\frac{x + 1}{2})^{2} + (\frac{y - 1}{4})^{2} = \frac{5}{16}

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

\frac{x ^{2}}{625} + \frac{y ^{2}}{400} = 1

What is ((x+2)^2)/4+((y-4)^2)/(20)=1 ?
The solution to ((x+2)^2)/4+((y-4)^2)/(20)=1 is Ellipse with (h,k)=(-2,4),a=2,b=2sqrt(5)