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

\frac{( x - 4 ) ^{2}}{4.5} + \frac{( y - 1 ) ^{2}}{1} = 1

y = \frac{2 x - 4}{- 2 y + 4} x + 6

x^{2} + 4 y^{2} + 9 x + 10 y - 14 = 0

\frac{( x + 1 ) ^{2}}{4} + \frac{( y - \frac{3}{2} ) ^{2}}{8} = 1

\frac{( x - 2 ) ^{2}}{4 ^{2}} + \frac{( y - 3 ) ^{2}}{5 ^{2}} = 1

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