Maths P3 May June 2009 P3

[sweetmariah10]

Question 6 ii and iii
And Question 9 ii ...... please ny kind brothere or sister out there could solve these two may june 2009 questions for me Alevel CIE

 

[CaptainDanger]

Help him out...

 

[ks136]

consult d book...u'll get d ans..i had the same prob 2

 

[intel1993]

Q9 ii) suppo0se the point on line where prependicular from p intersects = Q
the general cordinates of q will be same as of line only t will change for every point....
we have to find PQ magnitude so
pQ= OQ-Op
PQ= (4+2t 2-t -1-2t) - (0 2 4) eg: (x y z)
= (4+2t -t -5-2t)
now this vector is prep to the direction vector hence
PQ. D.V = 0
(4+2t -t -5-2t) . ( 2 -1 -2) =0
8+4t+t+10+4t= 0
t= -2....

now put t = -2 in pq vector it will becum ( 0 2 -1)
now take its magnitude it will be equal to UNDERROOT 5............ (PROVED)

 

[intel1993]

Q6 i) Dy/dx = -sint /cost

Q6 ii) y- (y1)= gradient(x- x1)
y- a sin^3t = -sint /cost (x- a cos^3t)
ycost - a sin^3t . cost = -x sint + a cos^3t sint
ycost +x sint = acos^3t sint + a sin^3t cost
ycost +x sint = acost sint( cos^2t + sin^2t) as ( cos^2t + sin^2t) = 1 Hence
ycost +x sint = acost sint


iii) when tangent meets the x axis y =0
xsint= acostsint
x= a cost

when tangent meets the y axis x=0

ycost= acost sint
y=a sint

Xy= (a^2 sin^2t + a^2 cos^2t)^ 1/2
Xy =( a^2(sin^2t + cos^2t) )^ 1 /2 as ( cos^2t + sin^2t) = 1 Hence
xy= a

 

[sweetmariah10]

Thank you soo much...God Bless u nd ur exams nd xtremepapers........Lots of love.... (L)

 

[CaptainDanger]