cambridge 4u helpppp (1 Viewer)

[conkerbuyore744]

can someone help me with these questions

on complex number
let h and k be points representing roots of x^2 + 2px +q = 0 where p and q are real and p^2 < q
find the algebraic relation satisfied by p and q in each of the following cases
(i) HOK is a right angle
(ii) A,B,H,K are equidistant from O

conics
question 11 and 12 on page 114
i cant really type the question onto here. ><


thanks!

 

[Affinity]

(i) If h=a+ib and k=c+id, the condition here is equivalent to ac + bd = 0

but a = c = -p and b = -d = sqrt(q-p^2) <-- (why?)

so this means that the condition is 2p^2 - q = 0, and we require also that q=/=0 (why?)

(ii) what's A and B?

need the questions to do it unfortunately

By the way, "If h=a+ib and k=c+id, the condition here is equivalent to ac + bd = 0"
can be shown by the fact that h=y*i*k for some real number y