Question

A straight line passes through the point (3,0) and meets a variable line y=tx at right angles at point P.Find the coordinates P in terms of t.Find also the value of k, given that P lies on the curve x²+y²=kx

Answer 1

i think this is the area of concern for the 2 lines

Answer 2

from geometry i recall a notion that any triangle that has the diameter of a circle for a hypot; and has legs that hit the outer circle; will always be a right triangle

Answer 3

so the circle that we are concerned with that matches the information is at least:

(x-1.5)^2 + y^2 = (1.5)^2

this traces all the points of perpendicular intersection of the 2 lines in question

Answer 4

Well I definitely know that a triangle with a hypotenuse is a right angled triangle,but what do you mean by the legs touching the outer circle ?

Answer 5

P =

Answer 6

i mean that where the other 2 sides meet up at to form a right angle will meet on the rim of the circle

Answer 7

now if we are looking for a circle that touches a specific spot ON this circle with the criteria that x^2 + y^2 = kx; then that circle will center at the origin

Answer 8

kx = r^2 ; 0 < r < 3
hmm

Answer 9

x^2 + y^2 = 1
--- ---
kx kx


x + y^2 = 1
- ---
k kx


1/k (x + y^2/x) = 1

1/k = 1/x+y^2/x

k = x+y^2/x

Answer 10

class beckons me; so good luck

Answer 11

What are the exact coordinates of P then ?