What is 16x^2+25y^2+100y=300 ?

The solution to 16x^2+25y^2+100y=300 is Ellipse with (h,k)=(0,-2),a=5,b=4

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16x^2+25y^2+100y=300

16 x^{2} + 25 y^{2} + 100 y = 300

(h, k) = (0, - 2), a = 5, b = 4

Solution steps

16 x^{2} + 25 y^{2} + 100 y = 300

Rewrite

16 x^{2} + 25 y^{2} + 100 y = 300

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 2), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, - 2), a = 5, b = 4

25 x^{2} + 4 y^{2} - 50 x + 8 y - 71 = 0

16 x^{2} - 64 x + 25 y^{2} + 100 y = 236

9 x^{2} + 11 y^{2} = 10

16 x^{2} + 36 y^{2} + 32 x + 72 y - 524 = 0

\frac{1}{3} 3 x^{2} + 3 y^{2} - 8 x - 8 y \cdot 31 = 0

What is 16x^2+25y^2+100y=300 ?
The solution to 16x^2+25y^2+100y=300 is Ellipse with (h,k)=(0,-2),a=5,b=4