What is the axis 16x^2+25y^2+32x-384=0 ?

The axis 16x^2+25y^2+32x-384=0 is semi-major axis a=5, semi-minor axis b=4

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axis 16x^2+25y^2+32x-384=0

axis

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

semi - major axis a = 5, semi - minor axis b = 4

Solution steps

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

Rewrite

16 x^{2} + 25 y^{2} + 32 x - 384 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 5, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), a = 5, b = 4

\frac{x ^{2}}{49} + \frac{y ^{2}}{36} = 1

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{9} = 1

\frac{x ^{2}}{8} + \frac{y ^{2}}{3} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{4} = 1

What is the axis 16x^2+25y^2+32x-384=0 ?
The axis 16x^2+25y^2+32x-384=0 is semi-major axis a=5, semi-minor axis b=4