the locus of the point of intersection of the tangents to the circle x=r cosy , y=r siny at the points whose parametric angles differ by pi/s is

a)x²+y²=r² b)x²+y²=2r² c)3(x²+y²)=2r² d)3(x²+y²)=4r²

Hi,

I think the s in pi/s is a no. But still i will tell you a general method to solve questions like these.

Take any point h,k which lies on our locus. Write the equation of pair of tangents from h,k to the circle by using SS1= T^2.

Now after simplification you will get a pair of straight lines which actually aree pair of tangents. It will be of form : ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0

Find the value of coefficients (a,b,h,f,g,c) by comapring the two equations.
The angles between the tangents will be 180 – (pi/s), let this be theta.

And we know that angle between straight lines is given by Tan(theta)= (h^2-ab)/(a+b).

Put the values, you will get the desired locus.