What is ((x-2)/9)^2+((y+2)/(25))^2=1 ?

The solution to ((x-2)/9)^2+((y+2)/(25))^2=1 is Ellipse with (h,k)=(2,-2),a=9,b=25

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((x-2)/9)^2+((y+2)/(25))^2=1

(\frac{x - 2}{9})^{2} + (\frac{y + 2}{25})^{2} = 1

(h, k) = (2, - 2), a = 9, b = 25

Solution steps

(\frac{x - 2}{9})^{2} + (\frac{y + 2}{25})^{2} = 1

Rewrite

(\frac{x - 2}{9})^{2} + (\frac{y + 2}{25})^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 2), a = 9, b = 25

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 2), b = 25, a = 9

25 x^{2} + 64 y^{2} - 400 x - 640 y + 1600 = 0

9 x^{2} + 25 y^{2} = 64

y^{2} = - 6 x^{2} + 4

x^{2} + 2 y^{2} + 2 x - 20 y = - 43

16 x^{2} + 16 y^{2} = 4 y^{2} + 20 y + 25

What is ((x-2)/9)^2+((y+2)/(25))^2=1 ?
The solution to ((x-2)/9)^2+((y+2)/(25))^2=1 is Ellipse with (h,k)=(2,-2),a=9,b=25