To determine the center and radius of the circle represented by the equation (x - 2)^2 + (x - 2)^2 = 5, we first need to rewrite the equation in standard form.
Expanding the terms, we have x^2 - 4x + 4 + x^2 - 4x + 4 = 5.
Combining like terms, we get 2x^2 - 8x + 8 = 5.
Subtracting 5 from both sides, we get 2x^2 - 8x + 3 = 0.
To find the center and radius, we can compare this equation to the standard form of the equation for a circle: (x - h)^2 + (y - k)^2 = r^2.
In this case, since the equation only involves the variable x, we can set y = 0.
Therefore, we have (x - h)^2 + (0 - k)^2 = r^2.
Comparing this equation to 2x^2 - 8x + 3 = 0, we can see that h = 2, k = 0, and r^2 = 3.
Thus, the center of the circle is (2, 0), and the length of the radius is √3.
Determine the centre of the circle and the length of the radius in the following:
a) (x - 2)^2 + (x - 2)^2 = 5
1 answer