What is (x^2)/9+((y+5)^2)/(25)=1 ?

The solution to (x^2)/9+((y+5)^2)/(25)=1 is Ellipse with (h,k)=(0,-5),a=3,b=5

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(x^2)/9+((y+5)^2)/(25)=1

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

(h, k) = (0, - 5), a = 3, b = 5

Solution steps

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

Rewrite

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 5), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 5), b = 5, a = 3

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{10} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{64} = 1

4 x^{2} + 3 y^{2} - 5 x + 2 y + 1 = 0

36 - 9 x^{2} - 4 y^{2} > 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{10} = 1

What is (x^2)/9+((y+5)^2)/(25)=1 ?
The solution to (x^2)/9+((y+5)^2)/(25)=1 is Ellipse with (h,k)=(0,-5),a=3,b=5