What is ((x+1)^2)/4+((y-5)^2)/9 =1 ?

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

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((x+1)^2)/4+((y-5)^2)/9 =1

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

(h, k) = (- 1, 5), a = 2, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 5), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 5), b = 3, a = 2

\frac{( x + 5 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{25} = 1

\frac{y ^{2}}{16} + \frac{x ^{2}}{9} = 1

0.25 x^{2} + y^{2} = 1

5 (x - 3)^{2} = 20 - 4 (y - 6)^{2}

16 x^{2} + 36 y^{2} = 576

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