Recent content by sooyong94

So any ideas to work it out then?

Homework Statement Show that the determinant of is (a-b)(b-c)(c-a) Homework Equations Row reduction, determinants The Attempt at a Solution Apparently I got a (a-b)^2 instead of (a-b) when I multiplied them up. It would be grateful if someone can point me out where the mistakes are.

Homework Statement Homework Equations Summation The Attempt at a Solution I know I could have simplified (3n-2)^3 +(3n-1)^3 -(3n)^3 and put the formulas in but I wonder is there any other method (I was thinking about grouping the terms, but to no avail) to work this out.

Homework Statement Find the equation of the tangents to the ellipse 4x^2+9y^2 = 36 which are equally inclined to the x and y-axis. Homework Equations Quadratic discriminant The Attempt at a Solution First I substituted y=mx+c into the ellipse, and determined its discriminant, and got c^2 =...

I'm sorry - but I can't catch it.

x=apq y=a(p+q)

Now I'm stuck on the second part: Show that the equation of the locus of the point of intersection of the tangents at P and Q to the parabola is y^2(x+2a)+4a^3 =0. What does this mean? Does this mean that the tangents at P and Q meet at a point? I managed to find the points of intersection...

Thanks - worked that out quickly.

Strangely enough I got this:

Homework Statement If the normal at P(ap^2 ,2ap) to the parabola y^2 = 4ax meets the curve again at Q(aq^2, 2aq), show that p^2 +pq+2=0 Homework Equations Point-slope form The Attempt at a Solution I tried putting y=2aq and x=aq^2 but I can seem to simplify the whole thing other than...

Looks like I managed to work them out. Please mark this thread as solved. ;)

Ah sorry about that.

Ah I see already - since 2F= 2F+6F/(k-1), when k is not equal to 1, it is divisible by 2.

2F+3(2F/(k-1) ?

k(k-1)(k+1) = 2F k^3 - k=2F k(k+1)(k+2) = k^3 +3k^2 +2k = k^3 - k +3k^2 +3k =2F+3k(k+1)