Coordinate Geometry
JUPEB Mathematics

Find the equation of the circle with centre $(1, -2)$ and radius $3$.

Find the perpendicular distance from the point $(3, 4)$ to the line $3x + 4y - 5 = 0$.

Find the angle that the line $y = \sqrt{3}\,x + 1$ makes with the positive $x$-axis.

Find the distance between the points $(1, 2)$ and $(4, 6)$.

Find the midpoint of the line segment joining $(-2, 3)$ and $(4, -1)$.

Find the gradient of the line passing through $(2, 3)$ and $(5, 9)$.

Find the equation of the line with gradient $3$ passing through the point $(1, 2)$.

Find the equation of the line perpendicular to $y = 2x + 3$ and passing through $(4, 1)$.

Find the point of intersection of the lines $y = 2x - 1$ and $y = -x + 5$.

Find the centre and radius of the circle $x^2 + y^2 - 4x + 6y - 12 = 0$.

Find the area of the triangle with vertices $(1, 1)$, $(4, 2)$ and $(2, 5)$.

Find the value of $k$ for which the line $kx + 3y = 6$ is parallel to the line $2x - y = 4$.