Question

Find the locus of a point which moves such that its distance from the point (0, 0) is twice its distance from the – axis.

Solution

Correct option is

Let P(x1, y1) be the moving point whose locus is required.

By hypothesis |OP| = 2|PM|                                                                                                                                                              

 

Squaring both sides then

                    

Changing (x1y1) to (x, y) then

                  

Which is the required locus of P.

                                                                              

 

SIMILAR QUESTIONS

Q1

If α, β, γ are the real roots of the equation x3 – 3px3 + 3qx – 1 = 0, then the centroid of the triangle with vertices 

Q2

The number of points (p, q) such that p, q Ïµ {1, 2, 3, 4} and the equation px2 + qx + 1 = 0 has real roots is

Q3

If G is the centroid and I the incentre of the triangle with vertices A(–36, 7), B(20, 7) and C(0, –8), then GI is equal to

Q4

Consider the point   then

Q5

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Q6

Find the co – ordinates of the point which divides the line segment joining the pints (5, – 2) and (9, 6) in the ratio 3 : 1.

Q7

Find the co – ordinates of a point which divides externally the line joining (1, 3) and (3, 9) in the ratio 1 : 3.

Q8

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

Q9

Find the area of the pentagon whose vertices are A(1, 1), B(7, 21), C(7, –3), D(12, 2) and (0, –3).

Q10

Find the equation of the curve 2x2 + y2 – 3+ 5– 8 = 0 when the origin is transferred to the point (–1, 2) without changing the direction of axes.