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

25 x^{2} + 50 x + 4 y^{2} - 16 y = 59

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

3 x^{2} + 8 y^{2} + 12 x + 48 y + 60 = 1

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

25 x^{(2)} + 16 y^{(2)} = 400

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