What is ((x+5)^2)/(97)+((y+2)^2)/(36)=1 ?

The solution to ((x+5)^2)/(97)+((y+2)^2)/(36)=1 is Ellipse with (h,k)=(-5,-2),a=sqrt(97),b=6

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((x+5)^2)/(97)+((y+2)^2)/(36)=1

\frac{( x + 5 ) ^{2}}{97} + \frac{( y + 2 ) ^{2}}{36} = 1

(h, k) = (- 5, - 2), a = 97, b = 6

Solution steps

\frac{( x + 5 ) ^{2}}{97} + \frac{( y + 2 ) ^{2}}{36} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{97} + \frac{( y + 2 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 97 ) ^{2}} + \frac{( y - ( - 2 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, - 2), a = 97, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, - 2), a = 97, b = 6

2 a^{2} + b^{2} = a + b

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

x^{2} + 3 (y^{2}) = 84

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

What is ((x+5)^2)/(97)+((y+2)^2)/(36)=1 ?
The solution to ((x+5)^2)/(97)+((y+2)^2)/(36)=1 is Ellipse with (h,k)=(-5,-2),a=sqrt(97),b=6