## How to Determine Odd Even Function

Here, you will learn what is odd even functions and how to determine if given function is odd or even with example. Let’s begin – Odd Even Function : Let a function f(x) such that both x and -x are in its domain then If f(-x) = f(x) then f is said to be an …

## Equation of Normal to Parabola in all Forms

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 : …

## Equation of Tangent to Parabola in all Forms

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 …

## Equation of Tangent to Hyperbola in all Forms

Equation of Tangent to Hyperbola $$x^2\over a^2$$ – $$y^2\over b^2$$ = 1 (a) Point form : The equation of tangent to the given hyperbola at its point ($$x_1, y_1$$) is $$x{x_1}\over a^2$$ – $$y{y_1}\over b^2$$ = 1 Example : Find the equation of tangent to the hyperbola $$16x^2$$ – $$9y^2$$ = 144 at (5, 16/3). …

## Equation of Normal to Hyperbola in all Forms

Equation of Normal to hyperbola : $$x^2\over a^2$$ – $$y^2\over b^2$$ = 1 (a) Point form : The equation of normal to the given hyperbola at the point P($$x_1, y_1$$) is $$a^2x\over x_1$$ + $$b^2y\over y_1$$ = $$a^2+b^2$$ = $$a^2e^2$$ Example : Find the equation of normal to the hyperbola $$x^2\over 25$$ – $$y^2\over 16$$ = …

## Equation of Tangent to Ellipse in all Forms

Equation of Tangent to Ellipse $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1 : (a) Point form : The equation of tangent to the given ellipse at its point ($$x_1, y_1$$) is  $$x{x_1}\over a^2$$ + $$y{y_1}\over b^2$$ = 1. Note – For general ellipse replace $$x^2$$ by $$xx_1$$, $$y^2$$ by $$yy_1$$, 2x by $$x + x_1$$, …

## Equation of Normal to Ellipse in all Forms

Equation of Normal to ellipse : $$x^2\over a^2$$ + $$y^2\over b^2$$ = 1 (a) Point form : The Equation of normal to the given ellipse at ($$x_1, y_1$$) is $$a^2x\over x_1$$ + $$b^2y\over y_1$$ = $$a^2-b^2$$ = $$a^2e^2$$ Example : Find the normal to the ellipse $$9x^2+16y^2$$ = 288 at the point (4,3). Solution : …

## What is the Formula for Integration by Parts ?

Formula for Integration by Parts If u and v are two functions of x, then the formula for integration by parts is – $$\int$$ u.v dx = u $$\int$$ v dx – $$\int$$[$$du\over dx$$.$$\int$$v dx]dx i.e The integral of the product of two functions = (first function) $$\times$$ (Integral of Second function) – Integral of …