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P(acos@,bsin@) lies on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1. The Normal at P cuts the x axis at X and the Y axis at Y. Show that (PX)/(PY)=(b^2)/(a^2) is the distance formula the only way to go about this one?

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if the sum of an arithmetic series S_n=n^2+2n find a formula for T_n, ie the nth term of the series

i) The complex numbers 2+1, -1-2i and z represent points A, B and C on the Argand Diagram. Find One Possible value of z such that Triangle ABC is right angled at C and |CB|=2|CA| ii) Given\ that\ p_n\ and\ q_n\ are\ integers,\ prove,\ by\ mathematical\ induction,\ that...

i) Solve cos3@-cos@=2sin@ for 0<@<2Pi ii) Solve 2|x|-|x-2|>2

i) If z is a complex number such that z=k(cos@+isin@), where k is real, show that arg(z+k)=@/2 ii) Deduce that if z1, z2 and z3 are ANY three complex numbers at the vertices of an equilateral triangle then (z1)^2+(z2)^2+(z3)^2=z1z2+z2z3+z1z3 iii) Given that 1+z+z^2+z^3=(1-z^4)/(1-z) and that...