Question

What are the center and the radius of the circle 4x2 + 4y2 - 8x + 16y -4 = 0?

Answer 1

Answer:

Center of circle: (1, -2)

Radius: √6

Step-by-step explanation:

First, we need to isolate the constant:

$4x^2 + 4y^2 - 8x + 16y = 4$

Then, we can divide the whole equation by 4:

$x^2+y^2-2x+4y=1$

Then, we can complete the square(reminder: (a+b)^2 = a^2 + 2ab + b^2)

$(x^2-2x)+(y^2+4y)=1\\(x^2-2x+1)+(y^2+4y)=1+1\\(x^2-2x+1)+(y^2+4y+4)=1+1+4\\(x-1)^2+(y+2)^2=6$

Now that we got the standard equation of the circle, we can find the center and radius by using the equation $(x-h)^2+(y-k)^2=r^2$, where (h, k) is the coordinate of the center, and r is the radius.

Therefore, the center of the circle is (1, -2), and the radius of the circle is √6.