Let `0-=(0,0),A-=(0,4),B-=(6,0)dot` Let `P` be a moving point such that the area of triangle `P O A` is two times the area of triangle `P O B` . The locus of `P` will be a straight line whose equation can be

if P,Q are two points on the line 3x+4y+15=0 such that OP=OQ=9 then the area of triangle OPQ is

Let A (-4,0) ,B(4,0) Number of points c= (x,y) on circle x^2+y^2=16 such that area of triangle whose verties are A,B,C is positive integer is:

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are (a) (4/3,3) (b) (3,2/3) (c) (3,4/3) (d) (4/3,2/3)

Consider the parabola y^(2)=4x , let P and Q be two points (4,-4) and (9,6) on the parabola. Let R be a moving point on the arc of the parabola whose x-coordinate is between P and Q. If the maximum area of triangle PQR is K, then (4K)^(1//3) is equal to

The area of the triangle formed by the points (0,0),(3,0) and (0,4) is :

A point P(x,y) moves that the sum of its distance from the lines 2x-y-3=0 and x+3y+4=0 is 7 . The area bounded by locus P is (in sq. unit)

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

Let A B be chord of contact of the point (5,-5) w.r.t the circle x^2+y^2=5 . Then find the locus of the orthocentre of the triangle P A B , where P is any point moving on the circle.

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is 1/(sqrt(3)) (b) -1/(sqrt(3)) 1/(sqrt(2)) (d) none of these

Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such that x y >0a n dx+y<1, then (a) P lies either inside the triangle O A B or in the third quadrant. (b) P cannot lie inside the triangle O A B (c) P lies inside the triangle O A B (d) P lies in the first quadrant only