Let us consider a point P with coordinates (x, y) on the parabola. When the axis of symmetry is along the y-axis, the parabola opens upwards if the coefficient of y is positive and opens downwards if the coefficient of y is negative.When the axis of symmetry is along the x-axis, the parabola opens to the right if the coefficient of the x is positive and opens to the left if the coefficient of x is negative.If the equation has the term with y 2, then the axis of symmetry is along the x-axis and if the equation has the term with x 2, then the axis of symmetry is along the y-axis.
Parabola is symmetric with respect to its axis. The following are the observations made from the standard form of equations: The transverse axis and the conjugate axis of each of these parabolas are different. The four standard forms are based on the axis and the orientation of the parabola. The below image presents the four standard equations and forms of the parabola. There are four standard equations of a parabola. Here are the formulas to find the equation of the axis, directrix, vertex, focus, and length of the latus rectum of different types of parabolas. The eccentricity of a parabola is equal to 1. It is the ratio of the distance of a point from the focus, to the distance of the point from the directrix. The endpoints of the latus rectum are (a, 2a), (a, -2a). The length of the latus rectum is taken as LL' = 4a. Latus Rectum: It is the focal chord that is perpendicular to the axis of the parabola and is passing through the focus of the parabola. The focal distance is also equal to the perpendicular distance of this point from the directrix. Focal Distance: The distance of a point \((x_1, y_1)\) on the parabola, from the focus, is the focal distance. The focal chord cuts the parabola at two distinct points. Focal Chord: The focal chord of a parabola is the chord passing through the focus of the parabola. The directrix is perpendicular to the axis of the parabola. Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. Focus: The point (a, 0) is the focus of the parabola. Some of the important terms below are helpful to understand the features and parts of a parabola y 2 = 4ax. The standard equation of a regular parabola is y 2 = 4ax. The general equation of a parabola is: y = a(x-h) 2 + k or x = a(y-k) 2 +h, where (h,k) denotes the vertex. Parabola is an important curve of the conic sections of the coordinate geometry. "A locus of any point which is equidistant from a given point ( focus) and a given line ( directrix) is called a parabola." Thus, a parabola is mathematically defined as follows: Also, an important point to note is that the fixed point does not lie on the fixed line. The fixed point is called the "focus" of the parabola, and the fixed line is called the "directrix" of the parabola. 
Or you can click on a topic link below Concept wise to learn the Teachoo way.A parabola refers to an equation of a curve, such that each point on the curve is equidistant from a fixed point, and a fixed line. Finding Area of Quadrialteral using Area of Triangle Formula (dividing Quadrilateral into 2 triangles and finding area)Ĭlick on an exercise link below to study from the NCERT Way.Proving 3 points collinear using Area of Triangle Formula.Finding Area of triangle when coordinates of all 3 vertices are given.Using properties of parallelogram to do some questions on Section Formula (like finding coordinates of a point, when 4 vertices of parallelogram are given).
Finding ratio when coordinates of point of intersection is given.Finding coordinates of mid-point of a line using Section Formula.Then, we will learn about Section Formula - Finding coordinates of a point that divides line joining two points in some ratio.Finding points equidistant to given points.Checking if 3 points are collinear using Distance Formula.(To do this, we need to learn properties of parallelogram) Checking if points form a triangle, or an isoceles triangle, or a square, rectangle.
How to find distance between two points using Distance Formula. Coordinates of points in x-axis (x, 0) and y-axis (0, y). In Coordinate Geometry of Class 9, we learned what is x and y coordinate of a point. All questions have been solved in an easy to understand way with detailed explanation of each and every step.Īnswers to optional exercise is also given Get NCERT Solutions of all Exercise Questions and Examples of Chapter 7 Class 10 Coordinate Geometry. Updated for new NCERT Book for 2023-2024 Boards.
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