A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,theta) be the polar coordinates of P, chosen so that r is positive and 0

Question

A circle C has center at the origin and radius 9. Another circle K has a diameter with one end at the origin and the other end at the point (0,17). The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,theta) be the polar coordinates of P, chosen so that r is positive and 0<theta<2 inclusive. Find r and theta.

bobpursley · Answer

WEll, r has to be 9(center with radius 9)

x^2+y^2=9
x^2+(y-17/2)^2= (289/4)
subtract the first equation from the second

(Y-17/2)^2-y^2=289/4 - 9
-17y+289/4=289/4-9
y= 9/17 at the point of intersection.

sinTheta= 9/17*3= 9/51
check my work.