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

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

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

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

(h, k) = (4, 5), a = 3, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, 5), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (4, 5), a = 3, b = 2

- 8 y^{2} + 72 = 9 x^{2}

\frac{( x + 3 ) ^{2}}{36} + \frac{( y - 4 ) ^{2}}{16} = 1

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

10 - \frac{x ^{2}}{2} - y^{2} = x^{2} + 4 y^{2}

x^{2} + 1 - 2 x + 4 y^{2} + 16 y > 0

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