What is ((x+5)^2)/(81)+((y-1)^2)/(144)=1 ?

The solution to ((x+5)^2)/(81)+((y-1)^2)/(144)=1 is Ellipse with (h,k)=(-5,1),a=9,b=12

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((x+5)^2)/(81)+((y-1)^2)/(144)=1

\frac{( x + 5 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{144} = 1

(h, k) = (- 5, 1), a = 9, b = 12

Solution steps

\frac{( x + 5 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{144} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{81} + \frac{( y - 1 ) ^{2}}{144} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 5, 1), a = 9, b = 12

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 5, 1), b = 12, a = 9

\frac{8 x}{x ^{2} + y ^{2} + 1} = 1

(16 - x^{2} - 9 y^{2}) = - 1

36 x^{2} + 17 y^{2} - 648 x + 238 y + 689 = 0

25 x^{2} + 16 y^{2} - 200 x - 160 y + 400 = 0

\frac{x ^{2}}{64} + \frac{( y - 6 ) ^{2}}{121} = 1

What is ((x+5)^2)/(81)+((y-1)^2)/(144)=1 ?
The solution to ((x+5)^2)/(81)+((y-1)^2)/(144)=1 is Ellipse with (h,k)=(-5,1),a=9,b=12