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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

36 X^{2} + 25 Y^{2} = 900

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{4 ^{2}} = 1

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

1 x^{2} + 3 y^{2} + 8 x + 9 y - 14 = 0

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