What is ((y-6)^2)/(36)+((x+3)^2)/(16)=1 ?

The solution to ((y-6)^2)/(36)+((x+3)^2)/(16)=1 is Ellipse with (h,k)=(-3,6),a=4,b=6

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((y-6)^2)/(36)+((x+3)^2)/(16)=1

\frac{( y - 6 ) ^{2}}{36} + \frac{( x + 3 ) ^{2}}{16} = 1

(h, k) = (- 3, 6), a = 4, b = 6

Solution steps

\frac{( y - 6 ) ^{2}}{36} + \frac{( x + 3 ) ^{2}}{16} = 1

Rewrite

\frac{( y - 6 ) ^{2}}{36} + \frac{( x + 3 ) ^{2}}{16} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{4 ^{2}} + \frac{( y - 6 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 6), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 6), b = 6, a = 4

\frac{x ^{2}}{9} + \frac{( y - 4 ) ^{2}}{7} = 1

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

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

9 x^{2} + 4 y^{2} - 126 x - 40 y + 505 = 0

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{25} = 1

What is ((y-6)^2)/(36)+((x+3)^2)/(16)=1 ?
The solution to ((y-6)^2)/(36)+((x+3)^2)/(16)=1 is Ellipse with (h,k)=(-3,6),a=4,b=6