1)a)Find the Cartesian equation of the curve represented x=1+4cosa, y= 4sina -2
b)Descibe the curve fully
c)Find the Cartesian equation of the locus of the point A (x,y) when the distance A from y=4 is twice the distance between A and the pont (2,-1)
x=1+4cosa ---> cosa = (x-1)/4
y= 4sina -2 ---> sina = (y+2)/4
sin^2 a + cos^2 a = 1
(x-1)^2/16 + (y+2)^2 /16 = 1
(x-1)^2 + (y+2)^2 = 16
looks like a circle with centre at (1,-2) and radius of 4
c) did you make a sketch?
let the point on y = 4 which is closest to A be P(x,4)
let Q be (2,-1)
so AP = 2AQ
√((x-x)^2 + (y-4)^2 ) = 2√((x-2)^2 + (y+1)^2 )
square both sides
(y-4)^2 = 4( (x-2)^2 + (y+1)^2 )
you finish it and sketch its curve.