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.
+128475 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
