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

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

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

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

(h, k) = (4, - 1), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (4, - 1), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (4, - 1), b = 3, a = 2

\frac{( x - 1.29 ) ^{2}}{1.17} + \frac{y ^{2}}{2.77} = 2

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

2 x^{2} + y^{2} - 5 = 1

5 (x + 1)^{2} + 3 y^{2} = 15

4 y^{(2)} + 2 x^{(2)} + 48 y + 4 x - 22 = 0

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