What is the axis 6.25x^2+16y^2-12.5x+64y-29.75=0 ?

The axis 6.25x^2+16y^2-12.5x+64y-29.75=0 is semi-major axis a=4, semi-minor axis b=2.5

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axis 6.25x^2+16y^2-12.5x+64y-29.75=0

axis

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

semi - major axis a = 4, semi - minor axis b = 2.5

Solution steps

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

Rewrite

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 2), a = 4, b = 2.5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 2), a = 4, b = 2.5

4 x^{2} + 49 y^{2} = 196

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{16} = 1

3 x^{2} + y^{2} - 24 x + 39 = 0

\frac{x ^{2}}{5} + \frac{y ^{2}}{9} = 1

36 x^{2} + 5 y^{2} - 90 y - 495 = 0

What is the axis 6.25x^2+16y^2-12.5x+64y-29.75=0 ?
The axis 6.25x^2+16y^2-12.5x+64y-29.75=0 is semi-major axis a=4, semi-minor axis b=2.5