Question

Find the equation of the locus of a moving point so that its distance from the point (1, 0) is always twice the distance from the point (0, –2).

Solution

Correct option is

3x2 + 3y2 + 2x + 16y + 15 = 0

Let (x1y1) be the coordinates of the moving point whose locus is to be found.

distance from (1, 0) = 2 × (distance from (0, –2))  

Replace x1 by x and y1 by y

Hence 3x2 + 3y2 + 2x + 16y + 15 = 0 is the equation of locus.

SIMILAR QUESTIONS

Q1

The number of integer values of m, for which the x-co-ordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:

Q2

The vertices of a triangles are A (x1x1 tan α), B (x2x2 tan β) and C (x3,x3 tan γ). If the circumcentre of Δ ABC coincides with the origin and H (ab) be its orthocenter, then a/b is equal to:

Q3

A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinates axes at points P and Q. As L varies, the absolute minimum values of OP + OQ is (O is origin)

 

 

Q4

Consider the family of lines 

           (x + y – 1) + λ (2x + 3y – 5) = 0

and   (3x + 2y – 4) + µ (x + 2y – 6) = 0  

equation of a straight line that belongs to both the families is:

Q5

If p1p2p3 be the length perpendicular from the points

(m2, 2m), (mm’m + m’) and (m’2, 2m’)

respectively on the line  

               

Q6

The point (a2a + 1) is a point in the angle between the lines 3x – y + 1 = 0 and x + 2y – 5 = 0 containing origin. Then ‘a’ belongs to the interval. 

Q7

Find all points on x + y = 4 that lie at a unit distance from the line 4x + 3y– 10 = 0.

Q8

Find the equation of the obtuse angle bisector of the lines 12x – 5y + 7 = 0 and 3y – 4x – 1 = 0.

Q9

Find the bisector of the acute angle between the line 3x + 4y = 11 and 12x – 5y = 2. 

Q10

A straight line drawn through point A (2, 1) making an angle π/4 with the +X-axis intersects another line x + 2y + 1= 0 in point B. Find the length AB.