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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,
⇒
Plugging the values of the angle, .
⇒ ...equation (ii)
Now re-arranging the equation (i) we can write it as,
⇒
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.
⇒
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).