Answer:
a)
is the equation of the curve that makes an angle π/3.
b)
is the equation of line through the point (4,4).
Step-by-step explanation:
Given:
A line from origin which makes an angle of
with x-axis.
A vertical line from
.
We have to write the equation of the curves in Polar or Cartesian format.
Step wise:
a) A line from origin which makes an angle of
with x-axis.
To write the equation of the above line in Polar coordinates is more desirable as the angles could be defined well in polar form.
So,
⇒
...equation (i)
⇒
...here
is the slope
The slope in terms of
(angle) can be written as,
⇒ ![tan(\theta)=\frac{y}{x}](https://tex.z-dn.net/?f=tan%28%5Ctheta%29%3D%5Cfrac%7By%7D%7Bx%7D)
Plugging the values of the angle,
.
⇒
...equation (ii)
Now re-arranging the equation (i) we can write it as,
⇒ ![y=\sqrt{3}\ (x)](https://tex.z-dn.net/?f=y%3D%5Csqrt%7B3%7D%5C%20%28x%29)
b) A vertical line from
.
<em>Note:</em>
<em>The equation of a vertical line always takes the form x = k, where k is any number and k is also the x-intercept .</em>
To write the above point in Cartesian coordinate is more acceptable and easy for us.
⇒ ![x=4](https://tex.z-dn.net/?f=x%3D4)
Then,
y = sq-rt(3) x is the equation of the curve that makes an angle π/3.
and x = 3 is the equation of line through the point (4,4).