What is ((x-2)^2)/4+((y+1)^2)/(16)=1 ?

The solution to ((x-2)^2)/4+((y+1)^2)/(16)=1 is Ellipse with (h,k)=(2,-1),a=2,b=4

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((x-2)^2)/4+((y+1)^2)/(16)=1

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

(h, k) = (2, - 1), a = 2, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 1), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), b = 4, a = 2

\frac{( ( x + 0 ) ^{2} )}{20} + \frac{( ( y + 0 ) ^{2} )}{16} = 1

x^{2} + 4 y^{2} - 4 x - 8 y = 0

x = \frac{x ^{2}}{16} + \frac{z ^{2}}{9}

4 x^{2} + 25 y^{2} + 549 = 72 x + 250 y

y^{2} = 16 - 6 x^{2}

What is ((x-2)^2)/4+((y+1)^2)/(16)=1 ?
The solution to ((x-2)^2)/4+((y+1)^2)/(16)=1 is Ellipse with (h,k)=(2,-1),a=2,b=4