Here you will learn how to find the focus of parabola with examples. Let’s begin – Focus of Parabola Coordinates (i) For Parabola \(y^2\) = 4ax : The coordinates of focus is (a, 0). (ii) For Parabola \(y^2\) = -4ax : The coordinates of focus is (-a, 0). (iii) For Parabola \(x^2\) = 4ay : […]
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Here you will learn formula for finding the equation of directrix of parabola with examples. Let’s begin – Equation of Directrix of Parabola (i) For Parabola \(y^2\) = 4ax : The equation of directrix is x = -a. (ii) For Parabola \(y^2\) = -4ax : The equation of directrix is x = a. (iii) For
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Here you will learn formula to find the length of latus rectum of parabola with examples. Let’s begin – Latus Rectum of Parabola A double ordinate through the focus is called the latus rectum i.e. the latus rectum of a parabola is a chord passing through the focus perpendicular to the axis. In the given
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Here you will learn what is the parametric equation of all forms of parabola and their parametric coordinates. Let’s begin – Parametric Equation of Parabola and Coordinates (i) For the parabola \(y^2\) = 4ax : The parametric equation is x = \(at^2\) & y = 2at. And parametric coordinates are (\(at^2\), 2at). (ii) For the
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Here you will learn some parabola examples for better understanding of parabola concepts. Example 1 : The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x – 4y + 3 = 0 is – Solution : The length of latus rectum = 2 x perp. from
Here, you will learn Different Types of Parabola and Standard equations of parabola, focal chord, double ordinate and latus rectum of parabola. Let’s begin – What is Parabola ? A parabola is the locus of a point which moves in a plane, such that its distance from a fixed point(focus) is equal to its perpendicular
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Here, you will learn general equation and formulas for conic sections and formula to distinguish between conic. Conic Sections A conic section, or conic is the locus of a point which moves in a plane so that its distance from a fixed point is in a constant ratio to its perpendicular distance from a fixed
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The equation of normal to parabola in point form, slope form and parametric form are given below with examples. Equation of Normal to Parabola \(y^2 = 4ax\) (a) Point form : The equation of normal to the given parabola at its point (\(x_1, y_1\)) is y – \(y_1\) = \(-y_1\over 2a\)(x – \(x_1\)) Example :
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The equation of tangent to parabola in point form, slope form and parametric form are given below with examples. Condition of Tangency for Parabola : (a) The line y = mx + c meets the parabola \(y^2\) = 4ax in two points real, coincident or imaginary according as a >=< cm \(\implies\) condition of tangency
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A parabola is locus of a point which moves in a plane, such that its distance from a fixed point called focus is equal to its perpendicular distance from a fixed straight line called directrix. Graph of a Parabola and their types are shown below. Basic Concepts of a Parabola (a) Focal distance : The
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