214k views
4 votes
A circle c has center at the origin and radius 5. another circle k has a diameter with one end at the origin and the other end at the point (0,18). 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,θ) be the polar coordinates of p, chosen so that r is positive and 0≤θ≤2. find r and θ.

1 Answer

1 vote
we know that

circle c
the center is the point (0,0)
radius r=5 units
equation of a circle c is
x²+y²=5²----------> x²+y²=25

circle k
has a diameter with one end at the origin and the other end at the point (0,18)
let
A (0,0) B(0,18)
the distance between A and B is the diameter
diameter=18----------> radius r=18/2-------> r=9 units

the center of circle k is the midpoint A and B
xm=0
ym=(18+0)/2=9
the center is the point (0,9)

the equation of a circle k is
x²+(y-9)²=9²----------> x²+(y-9)²=81

using a graph tool----------> calculate the point of intersection of circle c and circle k which lies in the first quadrant

see the attached figure
the solution is the point p (4.803,1.389)

calculate the polar coordinates of p---------> (r,θ)
r=
√[(4.803)²+(1.389)²]--------> r=5 units

tan θ=1.389/4.803-------> tan θ=0.28919
θ=arctan (0.28919)--------> θ=16.13°----------> 0.09pi

the solution is
r=5 units
θ=16.13° (0.09pi)

A circle c has center at the origin and radius 5. another circle k has a diameter-example-1
User RajeshKannan
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories