What is the axis 4x^2+25y^2+24x+250y=-561 ?

The axis 4x^2+25y^2+24x+250y=-561 is semi-major axis a=5, semi-minor axis b=2

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axis 4x^2+25y^2+24x+250y=-561

axis

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

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

Solution steps

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

Rewrite

4 x^{2} + 25 y^{2} + 24 x + 250 y = - 561

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{5 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, - 5), a = 5, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 5), a = 5, b = 2

16 x^{2} + 25 y^{2} + 224 x + 250 y - 191 = 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{49} = 1

\frac{( x + 1 ) ^{2}}{9} + \frac{( y + 3 ) ^{2}}{36} = 1

\frac{( x + 1 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{16} = 1

What is the axis 4x^2+25y^2+24x+250y=-561 ?
The axis 4x^2+25y^2+24x+250y=-561 is semi-major axis a=5, semi-minor axis b=2