What is (((x-2)^2))/((9))+(((y+5)^2))/((25))=1 ?

The solution to (((x-2)^2))/((9))+(((y+5)^2))/((25))=1 is Ellipse with (h,k)=(2,-5),a=3,b=5

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(((x-2)^2))/((9))+(((y+5)^2))/((25))=1

\frac{( ( x - 2 ) ^{2} )}{( 9 )} + \frac{( ( y + 5 ) ^{2} )}{( 25 )} = 1

(h, k) = (2, - 5), a = 3, b = 5

Solution steps

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

Rewrite

\frac{( x - 2 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 5), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 5), b = 5, a = 3

16 x^{2} + 25 y^{2} = 1400

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

(\frac{x}{16})^{2} + \frac{y ^{2}}{81} = 1

11 x^{2} + 5 y^{2} + 110 x - 20 y + 240 = 0

\frac{x ^{2}}{cosh ^{2} ( β )} + \frac{y ^{2}}{sinh ^{2} ( β )} = 1

What is (((x-2)^2))/((9))+(((y+5)^2))/((25))=1 ?
The solution to (((x-2)^2))/((9))+(((y+5)^2))/((25))=1 is Ellipse with (h,k)=(2,-5),a=3,b=5