Question

In polar coordinates, the parametric equations x=6+cos(f) and y=sin(f) represent a circle C1. In Cartesian coordinates, there is a circle C2 that is externally tangent to C1, tangent to the y-axis, and centered at (10,sqrt2). What is the value of a?

Answer 1

I assume a is the radius of C2.

since cos^2+sin^2 = 1,
C1 is (x-6)^2 + y^2 = 1

The distance between the centers of C1 and C2 is thus

d^2 = (10-6)^2 + (√2)^2 = 18

so, a+1 = √18, and a = √18 - 1

Answer 2

I made a small typing mistake. The center is (10,sqrta). so, what is a?

Answer 3

If C2 has center at (10,y) and touches the y-axis, its radius is 10.

Then distance between the circle centers is now

√(a+16) = 10+1 = 11
a+16 = 121
a = 105