What is ((x+1)^2)/5+((y-3)^2)/9 =1 ?

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

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((x+1)^2)/5+((y-3)^2)/9 =1

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

(h, k) = (- 1, 3), a = 5, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 3), a = 5, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 3), b = 3, a = 5

16 - 2 x^{2} - y^{2} > 0

x^{2} + 2 y^{2} + 4 x - 8 y - 6 = 0

8 x^{2} + 2 y^{2} - 32 = 0

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

16 x^{2} + 25 y^{2} - 96 x - 250 y + 369 = 0

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