Conics drawings... (1 Viewer)

[x.Exhaust.x]

1)a) Sketch, on the same set of axes, the graphs of x^2+y^2=b^2 and x^2+y^2=a^2, a>b.
b) Write down parametric equations for points Q and R on these circles respectively.
c) Comment on any similarities between these parametric equations and the parametric equations for a point P on the ellipse x^2/a^2+y^2/b^2=1.
d) On your sketch from part (a), construct several straight lines passing through the origin and these two concentric circles and label any points as Q and R as necessary.
e) For each pair of Qs and Rs on your sketch, label the point P corresponding to these Qs and Rs.
f) Trace out the locus of P.

A visual diagram would be sweet! Thanks.

 

[kaz1]

a)Looks like the graphs are concentric circles because they both have an eccentricity of 1 with the one with a² has a larger radius.
b)[acos(theta), asin(theta)] and [bcos(theta), bsin(theta)]
c) a and b are equal for the equations given

Can't be fucked drawing on a computer for d) and I don't get e) and f).

 

[jet]

a) These are concentric circles. You can see them below.
b) Q[acos(theta), asin(theta)], R[bcos(theta), bsin(theta)]
c)The point P has parametrics P[acos(theta), bsin(theta)]. It is obvious that the x-coordinate of P is the x-value of Q (the outer circle), whilst the y-coordinate of P is equal to the y-coordinate of R (the inner circle).
d) These lines represent differing values of theta.
e)The point P will be the point of intersection of the vertical line from Q and the horizontal line from R, where Q and R lie on the same straight line through the origin.
f)