A=(3,-1) and B is any point on the locus x*x+y*y=20.If seg.AB is extended to P such that AP=3.AB,find locus of P.
I have many such problems and dont know the answers.I have a test approaching and My teacher s.ucks.I am in XI and if u know the answer plz mail me-tejas_21b@yahoo.co.in.OR if u know any website 4 the locus questions tell me.THANX.
2006-08-10 03:59:41 · 3 answers · asked by tejas_fundo 3 in Science & Mathematics ➔ Mathematics
dont ask me to use google
2006-08-10 04:04:49 · update #1
Maybe you can use similar right triangles here, where AP and AB are the hypoteneuses.
B is on a circle centered at the origin: x^2 + y^2 = 20. Suppose B has the coordinates (a,b), and P is at (c,d). Then by similar triangles, AP/AB = (d + 1)/(b + 1) = (c - 3)/(a - 3) = 3.
d + 1 = 3(b + 1) = 3b + 3 ==> b = (d - 2)/3
c - 3 = 3(a - 3) = 3a - 9 ==> a = (c + 6)/3
b^2 = (d - 2)^2 / 9 = (d^2 - 4d + 4)/9
a^2 = (c + 6)^2 / 9 = (c^2 + 12c + 36)/9
But B = (a,b) is on the circle, so
a^2 + b^2 = 20 = [(c^2 + 12c + 36) + (d^2 - 4d + 4)]/9
Substitute x and y for c and d. I guess the best way to write it is by keeping the squares intact:
(x + 6)^2 + (y - 2)^2 = 180
That's the locus of P.
2006-08-10 06:22:33 · answer #1 · answered by bpiguy 7 · 1⤊ 0⤋
Dewd..... You need a tutor and you need one badly.
Those kinds of 'locus' problems tend to be straightforward, but real messy from a computational standpoint.
Doug
2006-08-10 11:26:51 · answer #2 · answered by doug_donaghue 7 · 0⤊ 1⤋
i have nooooo clue!!!! sry
2006-08-10 11:25:08 · answer #3 · answered by jazzyMS2013 1 · 0⤊ 0⤋