Category: 12. Analytic Geometry

The distance between a point and a line is defined to be the length of the perpendicular line segment connecting the point to the given line. Let (x1,y1) be the point not on the line and let (x2,y2) be the point on the line. To find the distance between the point (x1,y1)  and the line…

In order to derive the equation of an ellipse centered at the origin, consider an ellipse that is elongated horizontally into a rectangular coordinate system and whose center is placed at the origin. The foci are on the x-axis at (-c,0) and (c,0) and the vertices are also on the x-axis at (-a,0) and (a,0)…

By definition, a parabola is the set of all points (x,y) in a plane that are the same distance from a fixed line and a fixed point not on the line. The fixed point is the focus and the fixed line is the directrix. Take a look at the figure below and make note of…

The standard equation of a circle, also called the standard form, is (x – h)2 + (y – k)2 = r2. The radius of the circle is r, the center of the circle is (h , k), and (x , y) is any point on the circle. How to write the equation of a circle using the…

Finding the angle between two lines using a formula is the goal of this lesson. When two lines intersect in a plane, their intersection forms two pairs of opposite angles called vertical angles. If the two lines are not perpendicular and have slopes m1 and m2, then you can use the following formula to find the…

The inclination of a line or angle of inclination is the acute or obtuse angle that is formed when a nonhorizontal line intersects the x-axis. Formal definition: The inclination of a nonhorizontal line is the positive angle θ with θ less than 180 degrees and measured counterclockwise from the x-axis to the line. In the…