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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

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