P3 June 02 Parametric question

Please could someone tell me how to do this question, I have the answers, just dont know how to do it.


6. A curve is given parametrically by the equations
x = 5 cos t, y = -2 + 4 sin t, 0 £ t < 2p.

(a) Find the coordinates of all the points at which C intersects the coordinate axes, giving your answers in surd form where appropriate.
(4 marks)

Please could someone tell me how to do this question, I have the answers, just dont know how to do it.


6. A curve is given parametrically by the equations
x = 5 cos t, y = -2 + 4 sin t, 0 £ t < 2p.

(a) Find the coordinates of all the points at which C intersects the coordinate axes, giving your answers in surd form where appropriate.
(4 marks)

x=0 therefore cost = 0 => t = pi/2 or 3pi/2
y = 2 or -6 giving (0,2) and (0,-6)

y=0 => sint = 1/2 => t= pi/6 or 5pi/6
x = (root3)/2 and -(root3/2)

giving (root3/2,0) AND (-root3/2,0)

it is an ellipse

MB

x = 5 cos t, y = -2 + 4 sin t, 0 £ t < 2p.


wen x=0

5cos t = 0

cos t = 0

t = whatever

wen y=0

4sin t = 2

sint =0.5

t = pi / 6 or whatever it is

Tut tut!! BlueAngel hasn't got that far yet!!!!! You're jumping ahead!! lol

G

I understand that - when x = 5 cos t t = pi/2, and 3pi/2
when y = -2 + 4 sin t t = pi/6 etc...


But thats not the answer, the answer is (0, 2) , (0, -6) , (5root3/2, 0 ) , and (-5root3/2 , 0). Which I dont understand how you get.

I understand that - when x = 5 cos t t = pi/2, and 3pi/2
when y = -2 + 4 sin t t = pi/6 etc...


But thats not the answer, the answer is (0, 2) , (0, -6) , (5root3/2, 0 ) , and (-5root3/2 , 0). Which I dont understand how you get.

not posted before so i'm not sure if my notations are correct....but....

x=5cost
y=-2+4sint

x/5=cost
y+2/4=sint

using sin^2 t+cos^2t=1

(x/5)^2 + (y+2/4)^2=1

then substitute x=0 and y=0 into this equation and you get
y=-6 or y=2
and then x=+5root3/2 or -5root3/2

hope this helps

helen x

erm sorry if im wrong or something but
i agree that the parametric gives an elipse shape
but i dont think its in terms of pi

x = 5 cos t, y = -2 + 4 sin t

the furthest distance of x radius is 5
the furthest distance of y radius is 4

but the centre is (0,-2)

thats all i can say.
i hope i aint wrong..cause ive tried using this way in almost all of the past year questions and got most of it right