What is ((y+4)^2)/9+((x-9)^2)/(25)=1 ?

The solution to ((y+4)^2)/9+((x-9)^2)/(25)=1 is Ellipse with (h,k)=(9,-4),a=5,b=3

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((y+4)^2)/9+((x-9)^2)/(25)=1

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

(h, k) = (9, - 4), a = 5, b = 3

Solution steps

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

Rewrite

\frac{( y + 4 ) ^{2}}{9} + \frac{( x - 9 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 9 ) ^{2}}{5 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (9, - 4), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (9, - 4), a = 5, b = 3

\frac{( x - 100 ) ^{2}}{400} + \frac{( y - 90 ) ^{2}}{900} = 1

16 x^{2} + y^{2} = 64

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{9} = 1

4 x^{2} + 9 y^{2} - 24 x + 72 y + 144 = 0

What is ((y+4)^2)/9+((x-9)^2)/(25)=1 ?
The solution to ((y+4)^2)/9+((x-9)^2)/(25)=1 is Ellipse with (h,k)=(9,-4),a=5,b=3