What is ((x-4)^2}{36}+\frac{(y-2)^2)/6-1=0 ?

The solution to ((x-4)^2}{36}+\frac{(y-2)^2)/6-1=0 is Ellipse with (h,k)=(4,2),a=6,b=sqrt(6)

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((x-4)^2}{36}+\frac{(y-2)^2)/6-1=0

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{6} - 1 = 0

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

Solution steps

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{6} - 1 = 0

Rewrite

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{6} - 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

8 x^{(2)} + 2 y^{(2)} + 16 x = 0

2 x^{2} + 5 y^{2} + 3 x + 30 y - 16 = 0

8 x^{2} + y^{2} = 10

4 x^{2} + 7 y^{2} = 8

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{9} = 1

What is ((x-4)^2}{36}+\frac{(y-2)^2)/6-1=0 ?
The solution to ((x-4)^2}{36}+\frac{(y-2)^2)/6-1=0 is Ellipse with (h,k)=(4,2),a=6,b=sqrt(6)