What is the axis 4x^2-16x+25y^2+200y=-316 ?

The axis 4x^2-16x+25y^2+200y=-316 is semi-major axis a=5, semi-minor axis b=2

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axis 4x^2-16x+25y^2+200y=-316

axis

4 x^{2} - 16 x + 25 y^{2} + 200 y = - 316

semi - major axis a = 5, semi - minor axis b = 2

Solution steps

4 x^{2} - 16 x + 25 y^{2} + 200 y = - 316

Rewrite

4 x^{2} - 16 x + 25 y^{2} + 200 y = - 316

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

3 x^{(2)} + 2 y^{(2)} - 12 x + 8 y + 19 = 0

\frac{( x + 2 ) ^{2}}{4} + \frac{( y + 3 ) ^{2}}{9} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{9} = 4

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{4} = 1

3 x^{2} + 3 y^{2} - 18 y = 0

What is the axis 4x^2-16x+25y^2+200y=-316 ?
The axis 4x^2-16x+25y^2+200y=-316 is semi-major axis a=5, semi-minor axis b=2