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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(x - 1)^{2} + (y - 6)^{2} = 25

\frac{x ^{2}}{64} + \frac{y ^{2}}{36} = 1

x^{2} + 4 y^{2} = 16

(x - 6)^{2} + (y + 5)^{2} = 16

4 x^{2} + 4 y^{2} = 25

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