Coordinate geometry › Circles in coordinates

Centre and radius

Center of a circle from general form ●○○○○ 10 ptsFind the coordinates of the center of the circle $x^2 + y^2 - 4x + 2y - 1 = 0$ . Give the $x$ -coordinate and the $y$ -coordinate.
Centre of a circle from its equation ●○○○○ 10 ptsFind the coordinates $(a, b)$ of the centre of the circle $x^2+y^2+6x-8y-24=0$ .
Center of a circle through three points ●●○○○ 20 ptsA circle passes through the points $(-1, 2)$ , $(3,0)$ and $(9,0)$ . The center of the circle is at $(h,k)$ . Find the value of $h+k$ .
Area of circle through three points ●●○○○ 20 ptsA circle passes through the points $(1,1)$ , $(1,7)$ , and $(9,1)$ . The area of the circle can be expressed as $k\pi$ . Find the value of $k$ .
Hyperbola through three points ●●○○○ 20 ptsA hyperbola is centered at the origin and opens either horizontally or vertically. It passes through the points $(-3, 4)$ , $(-2, 0)$ , and $(t, 2)$ . Find $t^2$ .
Smallest integer-centred sphere through three points ●●●○○ 50 ptsA sphere has its center at a point with integer coordinates and passes through the three points $(2,0,0)$ , $(0,4,0)$ , $(0,0,6)$ , but does not pass through the origin $(0,0,0)$ . Let $r$ be the smallest possible radius of such a sphere. Compute $r^{2}$ .
Sums of squares on a unit circle ●●●○○ 50 ptsThree points $A(x_1, y_1)$ , $B(x_2, y_2)$ , $C(x_3, y_3)$ lie on the unit circle $x^2+y^2=1$ and satisfy $x_1+x_2+x_3=0$ and $y_1+y_2+y_3=0$ . Find $x_1^2+x_2^2+x_3^2$ and $y_1^2+y_2^2+y_3^2$ .
Center of a cube from three vertices ●●●○○ 50 ptsThree vertices of a cube in space have coordinates $A = (2,3,0)$ , $B = (0,5,4)$ , and $C = (4,1,8)$ . Find the coordinates $(x, y, z)$ of the center of the cube.

More in Circles in coordinates

Chord lengths Circles and the axes Distances between circles and lines Moving circles Points on a circle Radius from the equation Tangent circles