What is ((y-8)^2)/9+((x-5)^2)/4 =1 ?

The solution to ((y-8)^2)/9+((x-5)^2)/4 =1 is Ellipse with (h,k)=(5,8),a=2,b=3

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((y-8)^2)/9+((x-5)^2)/4 =1

\frac{( y - 8 ) ^{2}}{9} + \frac{( x - 5 ) ^{2}}{4} = 1

(h, k) = (5, 8), a = 2, b = 3

Solution steps

\frac{( y - 8 ) ^{2}}{9} + \frac{( x - 5 ) ^{2}}{4} = 1

Rewrite

\frac{( y - 8 ) ^{2}}{9} + \frac{( x - 5 ) ^{2}}{4} = 1

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{2 ^{2}} + \frac{( y - 8 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, 8), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, 8), b = 3, a = 2

0 = 4 x^{2} + y^{2} + 1

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

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

11 x^{2} + 13 y^{2} - 143 = 0

x^{2} + 3 y^{2} - 12 y + 9 = 0

What is ((y-8)^2)/9+((x-5)^2)/4 =1 ?
The solution to ((y-8)^2)/9+((x-5)^2)/4 =1 is Ellipse with (h,k)=(5,8),a=2,b=3