What is 4x^2+8y^2-4x-24y-13=0 ?

The solution to 4x^2+8y^2-4x-24y-13=0 is Ellipse with (h,k)=(1/2 , 3/2),a=2sqrt(2),b=2

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4x^2+8y^2-4x-24y-13=0

4 x^{2} + 8 y^{2} - 4 x - 24 y - 13 = 0

(h, k) = (\frac{1}{2}, \frac{3}{2}), a = 22, b = 2

Solution steps

4 x^{2} + 8 y^{2} - 4 x - 24 y - 13 = 0

Rewrite

4 x^{2} + 8 y^{2} - 4 x - 24 y - 13 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, \frac{3}{2}), a = 22, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, \frac{3}{2}), a = 22, b = 2

x^{2} + 16 y^{2} - 2 x - 64 y + 49 = 0

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

\frac{( x - 5 ) ^{2}}{2 ^{2}} + \frac{( y - 3 ) ^{2}}{9} = 1

25 x^{2} + 9 y^{2} + 100 x - 125 = 0

\frac{1}{x + i y} + \frac{1}{x - i y} < - 1

What is 4x^2+8y^2-4x-24y-13=0 ?
The solution to 4x^2+8y^2-4x-24y-13=0 is Ellipse with (h,k)=(1/2 , 3/2),a=2sqrt(2),b=2