Posted by Anonymous on Sunday, February 3, 2013 at 1:16pm.
A point is moving in a plane in such a way that its distance from the point(3,0)is 1.5 times its distance from the straight line 3x4=0.find the louces of the point and identify the conic.

geometry  Reiny, Sunday, February 3, 2013 at 4:01pm
let the point be P(x,y)
√((x3)^2+y^2) = 1.5(x4/3)
square both sides
(x3)^2 + y^2 = (9/4)(x^2  8x/3 + 16/9)
x^2  6x + 9 + y^2 = 9x^2/4  6x + 4
4x^2  24x + 36 + 4y^2 = 9x^2  24x + 16
5x^2  4y^2 = 20
or x^2 /4  y^2 /5 = 1 , which is a hyperbola
check my arithmetic
Answer This Question
Related Questions
 geometry  a point F is at a certain distance from a line AB .Another point P is...
 geometry  A small airplane takes off from point A and continues to climb upward...
 geometry  A small airplane takes off from point A and continues to climb upward...
 Geometry  A small airplane takes off from point A and continues to climb upward...
 physics  A toy plane p starts flying from point A along a straight horizontal ...
 Math  For each point in a set of points, its distance from (2,4) is three ...
 Add math  P(x,y) moves such that its distance from point Q(4,8)is twiceits ...
 Linear Algebra  In 3space, a plane abc is spanned by three points a, b, c. The...
 trigonometry  The angle of elevation of the top of a tower to point A on the ...
 Math  A line 'l' intersects line 'm' at point A at 45 degree angle. B and C are...
More Related Questions