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

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

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

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

(h, k) = (1, 2), a = 3, b = 23

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 2), a = 3, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 2), b = 23, a = 3

\frac{x ^{2}}{80} + \frac{y ^{2}}{12} = 1

36 x^{2} + 9 y^{2} = 324

4 y^{2} + 9 z^{2} = 36

3 (3 x^{2} + 9 y^{2} - 2 x - 36) = - 82

h (x) h (x) = - 5 x^{2} + 10 x + 15

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