What is the condition if a line touches the parabola?

If the discriminant of the resulting quadratic is positive, the line meets the parabola in two distinct points. If the discriminant of the resulting quadratic is zero, then the line is tangent to the parabola.

What do you call the fixed line of a parabola?

Key Concepts. A parabola is the set of all points (x,y) in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix. The standard form of a parabola with vertex (0,0) and the x-axis as its axis of symmetry can be used to graph the parabola.

What is Directrix parabola?

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.

Why is it called a tangent line?

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point. The word “tangent” comes from the Latin tangere, “to touch”.

Which of the following is the term used to refer to the chord that passes through the focus and is parallel to the fixed line?

The distance between the vertex and the focus, measured along the axis of symmetry, is the “focal length”. The “latus rectum” is the chord of the parabola that is parallel to the directrix and passes through the focus.

How do you get the end of latus rectum?

use h, k, and p to find the coordinates of the focus, (h,k+p) use k and p to find the equation of the directrix, y=k−p. use h, k, and p to find the endpoints of the latus rectum, (h±2p,k+p)

What is the name of the line and the point that a parabola is created from?

directrix
To form a parabola according to ancient Greek definitions, you would start with a line and a point off to one side. The line is called the “directrix”; the point is called the “focus”. The parabola is the curve formed from all the points (x, y) that are equidistant from the directrix and the focus.

What do you call a line that a curve approaches but does not intersect?

In geometry, an asymptote of a curve is a straight line that gets closer and closer but never touches the curve. An asymptote is sometimes called a tangent. An asymptote is a straight line, but specifically one that approaches or nears a curve but never meets it.

What is P in a parabola?

p is the distance from the vertex to the focus. You remember the vertex form of a parabola as being y = a(x – h)2 + k where (h, k) is the vertex of the parabola.

What are sideways parabolas called?

The important difference in the two equations is in which variable is squared: for regular (vertical) parabolas, the x part is squared; for sideways (horizontal) parabolas, the y part is squared. The “vertex” form of a parabola with its vertex at (h, k) is: regular: y = a(x – h)2 + k.

Why is it called the secant line?

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points. The word secant comes from the Latin word secare, meaning to cut. In the case of a circle, a secant intersects the circle at exactly two points.

How to find the tangent of a straight line to parabola?

Straight Line Touches a Parabola. The condition for a line y = m x + c to be a tangent to the parabola y 2 = 4 a x is that c = a m and the tangent to the parabola is y = m x + a m. Consider that the standard equation of a parabola with vertex at origin ( 0, 0) can be written as. y 2 = 4 a x – – – ( i) Also the equation of a line is represented by.

Which equation shows that y = mx + c touches the parabola?

Equation of tangent is y – 2a/m = m (x-a/my2) or y = mx + a/m Therefore, the condition that y = mx + c touches the Parabola

How to find the angle of intersection of two parabolas?

The angle between the tangents drawn to the two parabolas at the point of their intersection is defined as the angle of intersection of two parabolas. There can be various forms of equations of tangents to a parabola. We discuss these forms one by one: Suppose that the equation of a tangent to the parabola y2 = 4ax … (i) is y = mx + c. … (ii)

What is the dashed line with each parabola called?

The dashed line with each of these parabolas is called the axis of symmetry. Every parabola has an axis of symmetry and, as the graph shows, the graph to either side of the axis of symmetry is a mirror image of the other side.