What is ((y+16)^2)/(400)+(x^2)/(144)=1 ?

The solution to ((y+16)^2)/(400)+(x^2)/(144)=1 is Ellipse with (h,k)=(0,-16),a=12,b=20

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((y+16)^2)/(400)+(x^2)/(144)=1

\frac{( y + 16 ) ^{2}}{400} + \frac{x ^{2}}{144} = 1

(h, k) = (0, - 16), a = 12, b = 20

Solution steps

\frac{( y + 16 ) ^{2}}{400} + \frac{x ^{2}}{144} = 1

Rewrite

\frac{( y + 16 ) ^{2}}{400} + \frac{x ^{2}}{144} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 2 ^{2}} + \frac{( y - ( - 16 ) ) ^{2}}{2 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 16), a = 12, b = 20

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 16), b = 20, a = 12

\frac{( x + 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{49} = 1

16 - x^{2} - 9 y^{2} \geq 0

9 x^{2} + 6 y^{2} + 54 x - 36 y + 81 = 0

36 x^{2} + 25 y^{2} - 900 = 0

- 8 x^{2} - 2 y^{2} - 12 = 0

What is ((y+16)^2)/(400)+(x^2)/(144)=1 ?
The solution to ((y+16)^2)/(400)+(x^2)/(144)=1 is Ellipse with (h,k)=(0,-16),a=12,b=20