What is ((x-7)^2)/3+((y+11)^2)/5 =1 ?

The solution to ((x-7)^2)/3+((y+11)^2)/5 =1 is Ellipse with (h,k)=(7,-11),a=sqrt(3),b=sqrt(5)

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((x-7)^2)/3+((y+11)^2)/5 =1

\frac{( x - 7 ) ^{2}}{3} + \frac{( y + 11 ) ^{2}}{5} = 1

(h, k) = (7, - 11), a = 3, b = 5

Solution steps

\frac{( x - 7 ) ^{2}}{3} + \frac{( y + 11 ) ^{2}}{5} = 1

Rewrite

\frac{( x - 7 ) ^{2}}{3} + \frac{( y + 11 ) ^{2}}{5} = 1

in the form of the standard ellipse equation

\frac{( x - 7 ) ^{2}}{( 3 ) ^{2}} + \frac{( y - ( - 11 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (7, - 11), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (7, - 11), b = 5, a = 3

5 y (y + 4 x) + 4 x^{2} = - 20 (1 - x) y + 5

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

\frac{( x - 5 ) ^{2}}{12} + \frac{( y + 2 ) ^{2}}{16} = 1

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

x^{2} + 2 y^{2} - 10 x + 8 y + 29 = 0

What is ((x-7)^2)/3+((y+11)^2)/5 =1 ?
The solution to ((x-7)^2)/3+((y+11)^2)/5 =1 is Ellipse with (h,k)=(7,-11),a=sqrt(3),b=sqrt(5)