What is ((x+5)^2)/(25)+((y+1)^2)/(36)=1 ?

The solution to ((x+5)^2)/(25)+((y+1)^2)/(36)=1 is Ellipse with (h,k)=(-5,-1),a=5,b=6

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((x+5)^2)/(25)+((y+1)^2)/(36)=1

\frac{( x + 5 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{36} = 1

(h, k) = (- 5, - 1), a = 5, b = 6

Solution steps

\frac{( x + 5 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{36} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{5 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - 1), a = 5, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 1), b = 6, a = 5

x^{2} + 2 y^{2} = 2 x + 8

- 8 = 4 - 4 x^{2} - y^{2}

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

4 x^{2} + 9 y^{2} + 16 x + 18 y - 11 = 0

\frac{( ( x + 2 ) ^{2} )}{16} + \frac{( ( y - 4 ) ^{2} )}{4} = 1

What is ((x+5)^2)/(25)+((y+1)^2)/(36)=1 ?
The solution to ((x+5)^2)/(25)+((y+1)^2)/(36)=1 is Ellipse with (h,k)=(-5,-1),a=5,b=6