What is ((x-9)^2}{16}+\frac{(y-11)^2)/9 =1 ?

The solution to ((x-9)^2}{16}+\frac{(y-11)^2)/9 =1 is Ellipse with (h,k)=(9,11),a=4,b=3

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((x-9)^2}{16}+\frac{(y-11)^2)/9 =1

\frac{( x - 9 ) ^{2}}{16} + \frac{( y - 11 ) ^{2}}{9} = 1

(h, k) = (9, 11), a = 4, b = 3

Solution steps

\frac{( x - 9 ) ^{2}}{16} + \frac{( y - 11 ) ^{2}}{9} = 1

Rewrite

\frac{( x - 9 ) ^{2}}{16} + \frac{( y - 11 ) ^{2}}{9} = 1

in the form of the standard ellipse equation

\frac{( x - 9 ) ^{2}}{4 ^{2}} + \frac{( y - 11 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (9, 11), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (9, 11), a = 4, b = 3

1 - x^{2} - 5 y^{2} > 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{16} = 1

13 x^{2} + 4 y^{2} - 52 x - 24 y + 36 = 0

36 - 9 x^{2} - 4 y^{2} \geq 0

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

What is ((x-9)^2}{16}+\frac{(y-11)^2)/9 =1 ?
The solution to ((x-9)^2}{16}+\frac{(y-11)^2)/9 =1 is Ellipse with (h,k)=(9,11),a=4,b=3