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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

x^{2} + (8 - 6) y^{2} = 1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{9} = 1

\frac{100}{1 + x ^{2} + 2 y ^{2}} = 1

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