Let `O(0,0),A(2,0),a n dB(1, 1/(sqrt(3)))` be the vertices of a triangle. Let `R` be the region consisting of all those points `P` inside ` O A B` which satisfy `d(P , O A)lt=min[d(P, O B),d(P,A B)]` , where `d` denotes the distance from the point to the corresponding line. Sketch the region `R` and find its area.

Let A-=(6,7),B-=(2,3)a n dC-=(-2,1) be the vertices of a triangle. Find the point P in the interior of the triangle such that P B C is an equilateral triangle.

Two points O(0,0) and A(3,sqrt(3)) with another point P form an equilateral triangle. Find the coordinates of Pdot

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

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken inorder, find the value of p.

Let P(-9, 4, 5) and Q(11, 0, -1) be two given points. If O be the origin and ON be perpendicular to PQ then find the coordinates of N.

A point P(x ,y ,z) is such that 3P A=2P B , where Aa n dB are the point (1,3,4)a n d(1,-2,-1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.

P and Q are points on the line joining A(-2,5) and B(3,1) such that A P=P Q=Q B . Then, the distance of the midpoint of P Q from the origin is 3 (b) (sqrt(37))/2 (b) 4 (d) 3.5

For points P-=(x_1y_1) and Q-=(x_2,y_2) of the coordinate plane, a new distance d(P,Q) is defined by d (P,Q)=|X_1-X_2|+|y_1-y_2| Let O=(0,0),A=(1,2), B-=(2,3) and C-=(4,3) are four fixed points on x-y plane Answer the following questions based on above passage: Let R (x,y), such that R is equidistant from the points O and A with respect to new distance and if 0 < x < 1 and 0 < y < 2 then R lie on a line segment whose equation is

Let P(x) denote the probability of the occurrence of event xdot Plot all those point (x , y)=(P(A),P(B)) in a plane which satisfies the conditions, P(AuuB)geq3//4a n d1//8lt=P(AnnB)lt=3//8

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot