a) Show that the locus of points specified by π₯ = 3 cos π + 4 and π¦ = 3 sin π β 2 is a circle.

b) Find the equations of the tangents of the circle in a) at π = π/6 and π = 2π/ 3 and determine their point of intersection.

c) Another circle (π₯ β 1 2 )^2 + (π¦ β 3 2 )^2 = 25/ 2 intersects this circle at two points. Find the equation of the line through those two points.

Guest Jun 10, 2019

#1**+1 **

a) Show that the locus of points specified by π₯ = 3 cos π + 4 and π¦ = 3 sin π β 2 is a circle.

cos ΞΈ = (x - 4) /3 sin ΞΈ = (y + 2) / 3

And

cos^ΞΈ + sin^2ΞΈ = 1 ....so.....

(x - 4)^2 / 3^2 + (y + 2) /3^2 = 1

(x - 4)^2 + (y + 2)^2 = 3^2

(x -4)^2 + (y + 2)^2 = 9

This is a circle cenrered at ( 4, -2) with a radius of 3

CPhill Jun 10, 2019