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# cartesian equation circle question Watch

1. can someone help me solve this??
:show that the point (1/(1+t^2) , t/(1+t^2)) lies on a circle and hence find its centre and radius
2. (Original post by Carokelly123)
can someone help me solve this??
:show that the point (1/(1+t^2) , t/(1+t^2)) lies on a circle and hence find its centre and radius
Is that the whole question
3. (Original post by Carokelly123)
can someone help me solve this??
:show that the point (1/(1+t^2) , t/(1+t^2)) lies on a circle and hence find its centre and radius
What circle?
4. (Original post by 123Master321)
Is that the whole question
yeah it is!
5. (Original post by Carokelly123)
yeah it is!
Not enough information to define a circle.
6. (Original post by RDKGames)
Not enough information to define a circle.
Let me math a sec
7. (Original post by Carokelly123)
can someone help me solve this??
:show that the point (1/(1+t^2) , t/(1+t^2)) lies on a circle and hence find its centre and radius
Note that . Sub that expression for t into one of the expressions for x or y and then rearrange and you get the equation for a circle.
It's just converting from parametric to Cartesian.
8. (Original post by Carokelly123)
can someone help me solve this??
:show that the point (1/(1+t^2) , t/(1+t^2)) lies on a circle and hence find its centre and radius

Now you have two equations:

Rearrange one or both of the equations to get a function for t in terms of either X. Y or both, then substitute that function for t in the other. If the resulting equation is of the form:

Then you have a circle, centre and radius

EDIT: Note there is an easy method for this particular example to do the simultaneous equations.
9. t=y/x, substitute in x=1/(1+t^2) and rearrange to get x^2 - x +y^2 = 0, then complete the square to get (x-1/2)^2 + y^2 = (1/2)^2, i.e. a circle centered on (1/2, 0) with a radius of 1/2.
10. (Original post by RogerOxon)
t=y/x, substitute in x=1/(1+t^2) and rearrange to get x^2 - x +y^2 = 0, then complete the square to get (x-1/2)^2 + y^2 = (1/2)^2, i.e. a circle centered on (1/2, 0) with a radius of 1/2.

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Updated: October 17, 2016
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