It is given that `angleXYZ= 64^(@)` and XY is produced to point P. A ray YQ bisects `angleZYP`. Draw a figure from the given information. Find `angleXYQ` and reflex `angleQYP`.

In the given figure sides QP and RQ of ΔPQR are produced to points S and T respectively. If angleSPR = 135^(@) and anglePQT = 110^(@) , find anglePRQ.

A & B are two pts (0,2,3) and (2,-2,1) respectively find the locus of a point P such that it is equidistant from the given points

A and B are two points (0,2,3) and (2,-2,1) respectively. Find the locus of a point P such that the sum of the square of its distances from the two given points its constant, equal to 2k^2

P(-2,-3,6) is a given point and O is the origin. Find the coordinates of seven other points in three dimensional space such that the distance of each point from the origin O is equal to OP.

A straight line passes throught the point P(3,-2) and makes an angle theta with the positive direction of x - axis Find theta , given that the distance of P from the point of intersection of this line with the line 3x+4y=4 is (3sqrt(2))/(5) units.

Consider two lines L_1a n dL_2 given by x-y=0 and x+y=0 , respectively, and a moving point P(x , y)dot Let d(P , L_1),i=1,2, represents the distance of point P from the line L_idot If point P moves in a certain region R in such a way that 2lt=d(P , L_1)+d(P , L_2)lt=4 , find the area of region Rdot

In the given figure DeltaABC is equilateral on side AB produced. We choose a point such that A lies between P and B. We now denote 'a' as the length of sides of DeltaABC , r_1 as the radius of incircle DeltaPAC and r_2 as the ex-radius of DeltaPBC with respect to side BC. Then r_1 + r_2 is equal to

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is