What is ((x-6)^2)/(36)+((y+2)^2)/(100)=1 ?

The solution to ((x-6)^2)/(36)+((y+2)^2)/(100)=1 is Ellipse with (h,k)=(6,-2),a=6,b=10

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((x-6)^2)/(36)+((y+2)^2)/(100)=1

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1

(h, k) = (6, - 2), a = 6, b = 10

Solution steps

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1

Rewrite

\frac{( x - 6 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{100} = 1

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, - 2), a = 6, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (6, - 2), b = 10, a = 6

9 x^{2} - 72 x + 4 y^{2} + 40 y + 244 = 36

(x - a)^{2} + (y - (a - 16))^{2} = 1

3 x^{2} + 4 y^{2} + 6 x - 8 y - 5 = 0

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

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

What is ((x-6)^2)/(36)+((y+2)^2)/(100)=1 ?
The solution to ((x-6)^2)/(36)+((y+2)^2)/(100)=1 is Ellipse with (h,k)=(6,-2),a=6,b=10