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.

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.



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.


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 






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


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)


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


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


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


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 –


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 –


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


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



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