Dr. SK Goyal Solutions for Chapter: Coordinate Systems and Coordinates, Exercise 1: INTRODUCTORY EXERCISE 1.1

The transform equation of $r^2{\cos }^2\theta =a^2\cos 2\theta$ to Cartesian form is $\left(x^2+y^2\right)x^2=a^2\lambda$, then value of $\lambda$ is :

The co-ordinates of $P^{\text{'}}$ in the figure such that $OP=O{P}^{\text{'}}$ is :

The cartesian co-ordinates of the point $Q$ in the figure is :

A point lies on $x$-axis at a distance $5$ units from $y$-axis. What are its co-ordinates ?

A point lies on $y$-axis at a distance $4$ units from $x$-axis. What are its co-ordinates ?

A point lies on negative direction of $x$-axis at a distance $6$units from $y$-axis. What are its co-ordinates ?

Transform the equation $y=x\tan \alpha$ to polar form.

Transform the equation $r=2a\cos \theta$ to Cartesian form.