What is the axis (x+2)^2+((y+4)^2)/(1/4)=1 ?

The axis (x+2)^2+((y+4)^2)/(1/4)=1 is semi-major axis a=1, semi-minor axis b= 1/2

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axis (x+2)^2+((y+4)^2)/(1/4)=1

axis

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

semi - major axis a = 1, semi - minor axis b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, - 4), a = 1, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 4), a = 1, b = \frac{1}{2}

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

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

\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

What is the axis (x+2)^2+((y+4)^2)/(1/4)=1 ?
The axis (x+2)^2+((y+4)^2)/(1/4)=1 is semi-major axis a=1, semi-minor axis b= 1/2