Question

A straight line segment of length ‘p’ moves with its ends on two mutually perpendicular lines. find the locus of the point which divides the line in the ratio 1:2.

Solution

Correct option is

Choose the two mutually perpendicular lines as axes of coordinates.

The straight line segment AB of constant length ‘p’ slides so that A andB move along OX and OY respectively. Let P (x1y1) be a point of ABsuch that  

APPB = 1:2 it is required to find the locus of P

At any position of AB, let the intercepts OAOB be ab respectively, so that a2 + b2 = p2

Since AP : PB = 1 : 2, we have 

    

  

   

SIMILAR QUESTIONS

Q1

The number of straight lines equidistant from three non-collinear points in the plane of the points is equal to

Q2

A line bisecting the ordinate PN of a point P(at2, 2at), t > 0 on the parabola y2 = 4ax, a > 0 is drawn parallel to the axis to meet the curve at Q. If NQ and the tangent at the point P meet at, T, then the coordinates of point T is (where point N lie on the axis)

Q3

If the pair of line  intersect on x-axis, then α is equal to –

Q4

If the area of the rhombus enclosed by the lines  be 2 square units, then

Q5

If a2 + b2 – c2 – 2ab = 0 then the point of concurrency of family of straight lines ax + by + c = 0lies on the line –

Q6

All chords of the curve 3x2 – y2 –2x + 4y = 0 that subtends a right angle at the origin, pass through a fixed point whose co-ordinate is –

Q7

In a triangle ABC,  and point A lies on line y = 2x + 3 where  Area of  is such that [∆] = 5. Possible co-ordinates of ∆ is/are –

Q8

 then the point (x, y) lies on same side of the line 2x + y – 6 = 0 as the point –

Q9

Find the area of the quadrilateral with vertices (3, 3), (1, 4), (–2, 1), (2, –3).

 

Q10

Find the acute angle between the two lines with slopes 1/5 and 3/2.