What is ((x+2)^2)/(16)+((y+3)^2)/(36)=1 ?

The solution to ((x+2)^2)/(16)+((y+3)^2)/(36)=1 is Ellipse with (h,k)=(-2,-3),a=4,b=6

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((x+2)^2)/(16)+((y+3)^2)/(36)=1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{36} = 1

(h, k) = (- 2, - 3), a = 4, b = 6

Solution steps

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{36} = 1

Rewrite

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{36} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{6 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 3), a = 4, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 3), b = 6, a = 4

\frac{25 x ^{2}}{400 - 1 2 ^{2}} + \frac{16 y ^{2}}{400 - 1 2 ^{2}} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{225} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{169} + \frac{( y + 4 ) ^{2}}{144} = 1

9 x^{2} + 7 y^{2} = 42

What is ((x+2)^2)/(16)+((y+3)^2)/(36)=1 ?
The solution to ((x+2)^2)/(16)+((y+3)^2)/(36)=1 is Ellipse with (h,k)=(-2,-3),a=4,b=6