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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

25 x^{2} + 4 y^{2} - 50 x + 40 y = - 25

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

25 y^{2} + 12 x^{2} - 48 x - 75 y = 0

36 x^{2} + 64 y^{2} + 180 x - 256 y - 95 = 0

25 x^{2} + 9 y^{2} = 2245

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