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

5 y^{2} + 4 x^{2} = \frac{5}{4}

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

\frac{( x - 4 ) ^{2}}{12} + \frac{( y + 3 ) ^{2}}{16} = 1

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

2 x^{2} - 4 x + y^{2} + 2 y - 5 = 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