What is ((x+5)^2)/(20)+((y-6)^2)/(11)=1 ?

The solution to ((x+5)^2)/(20)+((y-6)^2)/(11)=1 is Ellipse with (h,k)=(-5,6),a=2sqrt(5),b=sqrt(11)

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((x+5)^2)/(20)+((y-6)^2)/(11)=1

\frac{( x + 5 ) ^{2}}{20} + \frac{( y - 6 ) ^{2}}{11} = 1

(h, k) = (- 5, 6), a = 25, b = 11

Solution steps

\frac{( x + 5 ) ^{2}}{20} + \frac{( y - 6 ) ^{2}}{11} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{20} + \frac{( y - 6 ) ^{2}}{11} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{( 2 5 ) ^{2}} + \frac{( y - 6 ) ^{2}}{( 11 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 6), a = 25, b = 11

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, 6), a = 25, b = 11

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

x^{2} + y^{2} + y^{2} = \frac{9}{4}

(x - 0.017)^{2} + (\frac{y ^{2}}{( 0.999 ) ^{2}}) = 1

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

(4 x^{2} - 8 x) + (9 y^{2} - 36 y) = - 4

What is ((x+5)^2)/(20)+((y-6)^2)/(11)=1 ?
The solution to ((x+5)^2)/(20)+((y-6)^2)/(11)=1 is Ellipse with (h,k)=(-5,6),a=2sqrt(5),b=sqrt(11)