Advertisements
Advertisements
Question
If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.
Solution
Let P(x, y) be a point on the required locus.
Then AP = 2BP, where A(2, 0) and B(0, 3)
∴ `sqrt((x - 2)^2 + (y - 0)^2) = 2sqrt((x - 0)^2 + (y - 3)^2`
On squaring both sides, we get,
(x – 2)2 + y2 = 4[x2 + (y – 3)2]
∴ x2 – 4x + 4 + y2 = 4(x2 + y2 – 6y + 9)
∴ x2 – 4x + 4 + y2 = 4x2 + 4y2 – 24y + 36
∴ 3x2 + 3y2 + 4x – 24y + 32 = 0
This is the required equation of the locus.
APPEARS IN
RELATED QUESTIONS
If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.
If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA2 = 3PB2
A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA2 − PB2 = 13
A(1, 6) and B(3, 5), find the equation of the locus of point P such that segment AB subtends right angle at P. (∠APB = 90°)
If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the point A(1, 3)
If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new coordinates of the point B(2, 5)
If the origin is shifted to the point O′(1, 3) the axes remaining parallel to the original axes, find the old coordinates of the point C(5, 4)
If the origin is shifted to the point O′(1, 3) the axes remaining parallel to the original axes, find the old coordinates of the point D(3, 3)
If the co-ordinates A(5, 14) change to B(8, 3) by shift of origin, find the co-ordinates of the point where the origin is shifted
Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:
3x − y + 2 = 0
Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:
x2 + y2 – 3x = 7
Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:
xy − 2x − 2y + 4 = 0
Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:
y2 − 4x − 4y + 12 = 0
If points (7, 6) and (-3, -4) lie on the locus ax + by = 6, then a and b are ______
If x coordinate of a point on the line joining points (2, 2, 1) and (5, 1, -2) is 4, then its z co-ordinate will be ______
If the origin is shifted to the point (2, 3), axes remaining parallel, then new co-ordinate of point (4,– 3) will be ______.
