What is ((x+5)^2)/(100)+((y-2)^2)/(36)=1 ?

The solution to ((x+5)^2)/(100)+((y-2)^2)/(36)=1 is Ellipse with (h,k)=(-5,2),a=10,b=6

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((x+5)^2)/(100)+((y-2)^2)/(36)=1

\frac{( x + 5 ) ^{2}}{100} + \frac{( y - 2 ) ^{2}}{36} = 1

(h, k) = (- 5, 2), a = 10, b = 6

Solution steps

\frac{( x + 5 ) ^{2}}{100} + \frac{( y - 2 ) ^{2}}{36} = 1

Rewrite

\frac{( x + 5 ) ^{2}}{100} + \frac{( y - 2 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 5 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - 2 ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 5, 2), a = 10, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 5, 2), a = 10, b = 6

\frac{y ^{2}}{36} + \frac{x ^{2}}{100} = 1

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

(x^{2} + 9 x) + (3 y^{2} + 10 y) = 2

\frac{x ^{2}}{100} + \frac{y ^{2}}{50} = 1

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

What is ((x+5)^2)/(100)+((y-2)^2)/(36)=1 ?
The solution to ((x+5)^2)/(100)+((y-2)^2)/(36)=1 is Ellipse with (h,k)=(-5,2),a=10,b=6