Question

Coordinate Geometry Help. *question attached* will give medal

Answer 1

(iii) Find the constants a, b and c such that x=b+acos(theta) and y=c+asin(theta) are parametric equations of C

Answer 2

How much work do you have on this problem thus far?

Answer 3

I have the first part. I found the coordinates of the centre, then substituted it into the equation of the line and it was true.

Answer 4

Sounds good to me. Alright, so you are then just starting with (ii)? Anything you've tried? Just to know where to begin. :)

Answer 5

I had no idea how to approach part (ii)

Answer 6

Well, when we usually want to find the intersection of two things -- say, two typical lines -- we solve a system of equations for the two variables.
Like, if we had y = -x + 4 and y = 3x + 4, we'd use some algebra to solve it like setting y=y and solving for x in a one-variable equation.

In terms of a line and a circle, we can do the same thing. The equation of a circle becomes the second equation, and we can use tricks like substitution to solve for the variables. Does that make sense?

Answer 7

Yes! Now that rang a bell :)

Answer 8

The only difference is that we will end up with multiple solutions, unlike two lines which have one intersection point.

Generally, this is going to be where you take the square root of squares and get plus AND minus solutions. (-b + OR - sqrt(b^2 ... etc.)

Answer 9

Okay :) Give me a second to work it out ^^