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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

64 xx - 256 x + 81 yy + 810 y = 2903

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

(\frac{x - 1}{36})^{2} + (\frac{y + 2}{25})^{2} = 1

9 x^{2} + 36 y^{2} + 36 x - 216 y + 36 = 0

\frac{( x - 4 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{1} = 1

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