Find parametric equations which describe each curve. No particular orientation is required. a. The line containing the points (1, 2) and (-3,8).
b. The circle with radius 3 and center (4,1).

The equation of the line is and the equation of the circle is .

Step-by-step explanation:

(a) Given: The given points are and .

To find: The parametric equation of line containing points and .

We know that the parametric equation of line containing and is given by where ∈.

Now,

i.e,

And,

i.e,

Hence, the required parametric equation of the line is .

(b) Given: The radius of circle is 3 and centre is .

To find: The parametric equation of circle with radius 3 and centre .

We know that parametric equation of circle with radius and centre is given by where and .

Now,

So, the parametric equation of circle having radius 3 and centre is .

Hence, the required equation of the circle is .

the answer is b.)

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