What is ((x-4)^2)/(16)+((y+2)^2)/(36)=1 ?

The solution to ((x-4)^2)/(16)+((y+2)^2)/(36)=1 is Ellipse with (h,k)=(4,-2),a=4,b=6

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((x-4)^2)/(16)+((y+2)^2)/(36)=1

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{36} = 1

(h, k) = (4, - 2), a = 4, b = 6

Solution steps

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{36} = 1

Rewrite

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - 4 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (4, - 2), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 2), b = 6, a = 4

What is ((x-4)^2)/(16)+((y+2)^2)/(36)=1 ?
The solution to ((x-4)^2)/(16)+((y+2)^2)/(36)=1 is Ellipse with (h,k)=(4,-2),a=4,b=6