What is ((x+2)^2)/(25)+((y-1)^2)/(169)=1 ?

The solution to ((x+2)^2)/(25)+((y-1)^2)/(169)=1 is Ellipse with (h,k)=(-2,1),a=5,b=13

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((x+2)^2)/(25)+((y-1)^2)/(169)=1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

(h, k) = (- 2, 1), a = 5, b = 13

Solution steps

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

Rewrite

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{169} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 5, b = 13

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), b = 13, a = 5

25 x^{2} + 4 y^{2} + 50 x - 16 y = 59

16 y^{2} + 25 x^{2} - 80 x + 36 y + 80 = 0

9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0

18 x^{2} + 8 y^{2} + 36 x - 32 y - 22 = 0

9 x^{2} + 4 y^{2} - 72 x - 24 y + 144 = 0

What is ((x+2)^2)/(25)+((y-1)^2)/(169)=1 ?
The solution to ((x+2)^2)/(25)+((y-1)^2)/(169)=1 is Ellipse with (h,k)=(-2,1),a=5,b=13