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a) Show that the locus of points specified by π‘₯ = 3 cos πœƒ + 4 and 𝑦 = 3 sin πœƒ βˆ’ 2 is a circle.

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

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

 Jun 10, 2019
 #1
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a) Show that the locus of points specified by π‘₯ = 3 cos πœƒ + 4 and 𝑦 = 3 sin πœƒ βˆ’ 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

 

 

cool cool cool

 Jun 10, 2019

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