Points of intersection of 2 curves

Find the coordinates of the points of intersection of the curve with parametric equations: , where with the line

What I have tried is to substitute x and y in with those in the parametric equations, but this forms which seems hard to solve, unless a graphical calculator is used.

Re: Points of intersection of 2 curves

Re: Points of intersection of 2 curves

Quote:

Originally Posted by

**Amer**
since i see

I think about an angle which has a value include

we have two angles

and

and I find that

fit for that

But when I sub them in x, the x-coordinates i get are 5.196 and 1 whereas the answer is 3.18. In addition, this is not a mathematical approach.

Re: Points of intersection of 2 curves

Ok

so now we have to curves see this link which solve these two curves and give x = which is equal to 5.196

Re: Points of intersection of 2 curves

Quote:

Originally Posted by

**Amer** Ok

so now we have to curves see this

link which solve these two curves and give x =

which is equal to 5.196

Thank you! However, the answer states x=3.18

Re: Points of intersection of 2 curves

I too get .

I began by eliminating the parameter θ.

Equating this to the given line, we find:

(1)

Squaring both sides (and being aware that extraneous solutions may be introduced):

Expanding gives:

Collecting like terms, rearranging and factoring yields:

By substitution into (1), we see x = 0 is an extraneous solution, so we need only consider:

This equation has two real roots, one of which is extraneous. By substitution into (1), we find the only valid root is:

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Re: Points of intersection of 2 curves

the graph shows three solutions ...

x = 0 , x = 3.18 , x = 5.196

Re: Points of intersection of 2 curves

I see now where I erred...

I failed to account for:

which would lead to:

(1)

where in addition, we also have the solutions:

My apologies for bungling my first post here!(Shake)