What is ((x-5)^2)/(144)+((y+2)^2)/(169)=1 ?

The solution to ((x-5)^2)/(144)+((y+2)^2)/(169)=1 is Ellipse with (h,k)=(5,-2),a=12,b=13

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((x-5)^2)/(144)+((y+2)^2)/(169)=1

\frac{( x - 5 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{169} = 1

(h, k) = (5, - 2), a = 12, b = 13

Solution steps

\frac{( x - 5 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{169} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{144} + \frac{( y + 2 ) ^{2}}{169} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (5, - 2), a = 12, b = 13

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, - 2), b = 13, a = 12

4 y^{(2)} + 2 x^{(2)} - 4 y - 8 x - 15 = 0

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

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

9 x^{2} + 5 y^{2} - 18 x - 40 y + 44 = 0

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

What is ((x-5)^2)/(144)+((y+2)^2)/(169)=1 ?
The solution to ((x-5)^2)/(144)+((y+2)^2)/(169)=1 is Ellipse with (h,k)=(5,-2),a=12,b=13