The equation of normal to parabola in point form, slope form and parametric form are given below with examples. Equation of Normal to Parabola y2=4ax (a) Point form : The equation of normal to the given parabola at its point (x1,y1) is y – y1 = −y12a(x – x1) Example : […]
Equation of Normal to Parabola in all Forms Read More »
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 y2 = 4ax in two points real, coincident or imaginary according as a >=< cm ⟹ condition of tangency
Equation of Tangent to Parabola in all Forms Read More »
Equation of Tangent to Hyperbola x2a2 – y2b2 = 1 (a) Point form : The equation of tangent to the given hyperbola at its point (x1,y1) is xx1a2 – yy1b2 = 1 Example : Find the equation of tangent to the hyperbola 16x2 – 9y2 = 144 at (5, 16/3).
Equation of Tangent to Hyperbola in all Forms Read More »
Equation of Normal to hyperbola : x2a2 – y2b2 = 1 (a) Point form : The equation of normal to the given hyperbola at the point P(x1,y1) is a2xx1 + b2yy1 = a2+b2 = a2e2 Example : Find the equation of normal to the hyperbola x225 – y216 =
Equation of Normal to Hyperbola in all Forms Read More »
Equation of Tangent to Ellipse x2a2 + y2b2 = 1 : (a) Point form : The equation of tangent to the given ellipse at its point (x1,y1) is xx1a2 + yy1b2 = 1. Note – For general ellipse replace x2 by xx1, y2 by yy1, 2x by x+x1,
Equation of Tangent to Ellipse in all Forms Read More »
Equation of Normal to ellipse : x2a2 + y2b2 = 1 (a) Point form : The Equation of normal to the given ellipse at (x1,y1) is a2xx1 + b2yy1 = a2−b2 = a2e2 Example : Find the normal to the ellipse 9x2+16y2 = 288 at the point (4,3). Solution :
Equation of Normal to Ellipse in all Forms Read More »
Let →a, →b, →c be three vectors. Then the scalar (→a×→b).→c is called the scalar triple product of →a, →b and →c and is denoted by [→a →b →c]. Thus, we have [→a →b →c] = (→a×→b).→c For three vectors →a, →b & →c, it is also defined as : (→a×→b).→c = \(|\vec{a}||\vec{b}||\vec{c}|sin\theta
What is Scalar Triple Product – Properties and Examples Read More »
Here you will learn what is domain, codomain and range of function and how to find domain and range of function with example. Let’s begin – Let f : A → B is a function. Then, the set A is known as the domain of f and the set B is known as the codomain
How to Find Domain and Range of Function Read More »
Formula for Integration by Parts If u and v are two functions of x, then the formula for integration by parts is – ∫ u.v dx = u ∫ v dx – ∫[dudx.∫v dx]dx i.e The integral of the product of two functions = (first function) × (Integral of Second function) – Integral of
What is the Formula for Integration by Parts ? Read More »
Earlier we find Area of Triangle by using the formula – Area of Triangle = √s(s−a)(s−b)(s−c) where s = a+b+c2 and a, b, c are the sides of the triangle. we have used this heron’s formula to find the area of a triangle when the lengths of its sides are given. Here, we will
Formula for Triangle Area Read More »
