## Equation of Normal to a Circle with Examples

The normal at a point is the straight line which is perpendicular to the tangent to circle at the point of contact. Normal at a point of the circle passes through the center of circle. Here, you will learn how to find equation of normal to a circle with example. Equation of Normal to a …

## Equation of Tangent to a Circle – Condition of Tangency

When a straight line meet a circle on two coincident points then it is called the tangent to a circle. Here, you will learn condition of line to be a tangent  to a circle and equation of tangent to a circle with example. Condition of Tangency : The line L = 0 touches the circle …

## 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 Scalar Triple Product – Properties and Examples

Let $$\vec{a}$$, $$\vec{b}$$, $$\vec{c}$$ be three vectors. Then the scalar $$(\vec{a}\times \vec{b}).\vec{c}$$ is called the scalar triple product of $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ and is denoted by [$$\vec{a}$$ $$\vec{b}$$ $$\vec{c}$$]. Thus, we have  [$$\vec{a}$$ $$\vec{b}$$ $$\vec{c}$$] = $$(\vec{a}\times \vec{b}).\vec{c}$$ For three vectors $$\vec{a}$$, $$\vec{b}$$ & $$\vec{c}$$, it is also defined as : ($$\vec{a}\times\vec{b}$$).$$\vec{c}$$ = \(|\vec{a}||\vec{b}||\vec{c}|sin\theta …