## 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 …

## Formula for Triangle Area

Earlier we find Area of Triangle by using the formula – Area of Triangle = $$1\over 2$$ $$\times$$ Base $$\times$$ Altitude 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 learn what is the formula for triangle area in terms …

## How to Find the Distance Between Two Parallel Lines

Distance Between Two Parallel Lines If two lines are parallel, then they have the same distance between them throughout, Therefore the distance between two parallel lines  $$ax + by + c_1$$ and $$ax + by + c_2$$ is given by : D = $$|c_1 – c_2|\over \sqrt{a^2 + b^2}$$ Note – Both equation must be …

## Cross Product of Vectors Formula [ Vector Product ]

Cross Product of Vectors Formula : Let $$\vec{a}$$ & $$\vec{b}$$ are two vectors & $$\theta$$ is the angle between them, then cross product of vectors formula is, $$\vec{a}$$ $$\times$$ $$\vec{b}$$ = |$$\vec{a}$$||$$\vec{b}$$|sin$$\theta$$$$\hat{n}$$ where $$\hat{n}$$ is the unit vector perpendicular to both $$\vec{a}$$ & $$\vec{b}$$. Properties of Vector Cross Product : (i) $$\vec{a}$$ $$\times$$ $$\vec{b}$$ = …

## How to Find General Solution of Trigonometric Equation

Here, you will learn what is trigonometric equation and how to find general solution of trigonometric equation with examples. Let’s begin – An equation involving one or more trigonometrical ratios of unknown angles is called a trigonometrical equation. Solution of Trigonometric Equation A value of the unknown angle which satisfies the given equation is called …