If A (2,0) And (0,2) Are Given Points And p is A Point Such That PA:PB = 2:3 Then The Locus Of p passes Through The Point (a,a) For

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.



If a (2,0) and (0,2) are given points and p is a point such that PA:PB = 2:3 then the locus of p passes through the point (a,a) for


Correct option is

No real value of a

Let p(x, y) be such that PA:PB = 2:3


     9(PA)2 = 4(PB)2

⇒ 9[(x – 2)y2] = 4[x2 + (y – 2)2]

⇒ 9(x2 + y2 – 4x +4) = 4(x2 + y2 – 4x + 4)

⇒ 5x + 5y 2 – 36x  + 16y + 20 = 0

Which is the locus of p and it passes through (a,a)if

     5a2 + 5a2 – 36a + 16a + 20 = 0

                       10a2 – 20a + 20 = 0

                               (a – 1)2 + 1= 0

Which is not possible for any real value of a.



ABCD is a rectangle with A(–1,2),B(3,7) and AB : BC = 4:3. If isthe center of the rectangle then the distance of p from each corner is equal to


A(1, 3), B(3, 7) & C(7, 15) are three points. P is the midpoint of ABQ is the midpoint of BC. Locus of a point R which satisfies (PR)2 – (QR)= (AC)2 is


If A(1, a), B(a, a2), C(a2, a2) are the vertices of a triangle which are equidistance from the origin, then the centroid of the triangle ABC is at the point


Given the point A(0, 4) and B(0, –4), the equation of the locus of the pointp(x, y) such that |AP – BP| = 6 is


Coordinate (x, y) of a point P satisfy the relation 3x + 4= 9, y = mx + 1. The number of integral value of m for which the x-coordinate of p is also an integer is


The point A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that 


Q, R and are the points on the line joining the points P(a, x) and T(b, y) such that PQ = QR = RS = ST.


The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then 


OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis


If px1x2….xi,….and q y1y2,…y… are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point Ai (xi, yi), = 1, 2 …n is