Coordinate Geometry

The center of the circle x^2 + y^2 - 4x + 6y - 12 = 0 is:

The radius of the circle x^2 + y^2 = 49 is:

Find the value of p if the points (1, 1), (2, 3), and (3, p) are collinear.

What is the distance between the points (a cos theta, a sin theta) and (0, 0)?

If the point (x, y) is equidistant from (5, 1) and (-1, 5), then:

The ratio in which the y-axis divides the line segment joining (2, -3) and (5, 6) is:

The equation of a line which makes equal intercepts on the axes and passes through (2, 3) is:

Find the slope of a line which is perpendicular to the line joining (0, 0) and (2, 2).

What is the length of the perpendicular from origin to the line 3x + 4y - 10 = 0?

Find the angle between the lines x + y = 5 and x - y = 3.

If (a, 0), (0, b), and (1, 1) are collinear, then 1/a + 1/b = ?

Find the coordinates of the circumcenter of a triangle with vertices (0,0), (8,0), and (0,6).

The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is:

Find the equation of a circle with center (2, -3) and radius 5.

If the line y = mx + c is a tangent to the circle x^2 + y^2 = a^2, then the condition is:

What is the area of a circle whose equation is x^2 + y^2 - 4x - 6y - 3 = 0?

Find the equation of the locus of a point which moves such that its distance from the y-axis is twice its distance from the x-axis.

The reflection of the point (3, 4) in the line y = x is:

Find the image of point (1, 2) when reflected across the x-axis.

What is the gradient of a line making an angle of 135 degrees with the x-axis?