What is the axis ((x+1)^2)/(64)+((y-1)^2)/(100)=1 ?

The axis ((x+1)^2)/(64)+((y-1)^2)/(100)=1 is semi-major axis b=10, semi-minor axis a=8

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axis ((x+1)^2)/(64)+((y-1)^2)/(100)=1

axis

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{100} = 1

semi - major axis b = 10, semi - minor axis a = 8

Solution steps

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{100} = 1

Rewrite

\frac{( x + 1 ) ^{2}}{64} + \frac{( y - 1 ) ^{2}}{100} = 1

in the form of the standard ellipse equation

\frac{( x - ( - 1 ) ) ^{2}}{8 ^{2}} + \frac{( y - 1 ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 8, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = 10, a = 8

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

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

What is the axis ((x+1)^2)/(64)+((y-1)^2)/(100)=1 ?
The axis ((x+1)^2)/(64)+((y-1)^2)/(100)=1 is semi-major axis b=10, semi-minor axis a=8