What is 16x^2+80y^2=1280 ?

The solution to 16x^2+80y^2=1280 is Ellipse with (h,k)=(0,0),a=4sqrt(5),b=4

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16x^2+80y^2=1280

16 x^{2} + 80 y^{2} = 1280

(h, k) = (0, 0), a = 45, b = 4

Solution steps

16 x^{2} + 80 y^{2} = 1280

Rewrite

16 x^{2} + 80 y^{2} = 1280

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 4 5 ) ^{2}} + \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 45, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 45, b = 4

\frac{5 x ^{2} + y ^{2} - 15 x + 8 y - 11}{4} = 0

\frac{x ^{2} + y ^{2} + 4 x - 8 y - 6}{x ^{2} + y ^{2} + 6 x + 2 y + 9} = \frac{4}{5}

64 - 25 x^{2} - 4 y^{2} + 24 y \geq 0

25 (x + 2)^{2} + 4 (y - 3)^{2} = 100

(x + 5)^{2} + 4 (y - 4)^{2} = 16

What is 16x^2+80y^2=1280 ?
The solution to 16x^2+80y^2=1280 is Ellipse with (h,k)=(0,0),a=4sqrt(5),b=4