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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} - 16 x + y^{2} + 2 y = - 1

4 x^{2} + 9 y^{2} = 4

2 x^{2} + 3 y^{2} = 1

\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y + k ) ^{2}}{b ^{2}} = 1

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

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