What is 16x^2+25(y+3)^2=1600 ?

The solution to 16x^2+25(y+3)^2=1600 is Ellipse with (h,k)=(0,-3),a=10,b=8

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16x^2+25(y+3)^2=1600

16 x^{2} + 25 (y + 3)^{2} = 1600

(h, k) = (0, - 3), a = 10, b = 8

Solution steps

16 x^{2} + 25 (y + 3)^{2} = 1600

Rewrite

16 x^{2} + 25 (y + 3)^{2} = 1600

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 0 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{8 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 10, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), a = 10, b = 8

\frac{( x - ( - 1.32 ) ) ^{2}}{3.78} + \frac{y ^{2}}{1.56} = 2

\frac{x ^{2}}{16} - \frac{x}{8} + 9 y^{2} - 18 y + \frac{17}{2} = 0

12 x^{2} + y^{2} = 16

3 x^{2} + y^{2} - 2 x + 60 y + 116 = x - 2 y - 4

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{3 ^{2}} = 1

What is 16x^2+25(y+3)^2=1600 ?
The solution to 16x^2+25(y+3)^2=1600 is Ellipse with (h,k)=(0,-3),a=10,b=8