What is ((x-6)^2)/(36)+((y+4)^2)/(16)=1 ?

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

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((x-6)^2)/(36)+((y+4)^2)/(16)=1

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 4 ) ^{2}}{16} = 1

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

Solution steps

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 4 ) ^{2}}{16} = 1

Rewrite

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 4 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

49 x^{2} + 9 y^{2} = 16

\frac{( x - 3 ) ^{2}}{36} + \frac{( y - 3 ) ^{2}}{32} = 1

x^{2} + 4 y^{2} - 20 x + 84 = 0

(x^{2} + y^{2} - 16 x + 8 y + 80) = 4 (x^{2} + y^{2} - 4 x - 8 y + 20)

16 (x - 2)^{2} + 25 (y + 3)^{2} = 124

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