Point P divides the line segment joining the points A(2,1) and B(5,−8) such that ABAP=31. If P lies on the line 2x−y+k=0, find the value of k.
What does the equation 2x2+4xy−5y2+20x−22y−14=0 become when referred to the rectangular axes through the point (−2,−3) , the new axes being inclined at an angle at 450 with the old axes?
Determine x so that the line passing through (3,4)and(x,5) makes an angle of 1350 with the positive direction of the x-axis.
Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, 3) and B is (1, 4).
The vertices of a triangle are [at1t2,a(t1+t2)], [at2t3,a(t2+t3)], [at3t1,a(t3+t1)] Then the orthocenter of the triangle is (a) (−a,a(t1+t2+t3)−at1t2t3) (b) (−a,a(t1+t2+t3)+at1t2t3) (c) (a,a(t1+t2+t3)+at1t2t3) (d) (a,a(t1+t2+t3)−at1t2t3)
A light ray emerging from the point source placed at P(2,3) is reflected at a point Q on the y-axis. It then passes through the point R(5,10)˙ The coordinates of Q are (0,3) (b) (0,2) (0,5) (d) none of these
In which quadrant or on which axis do each of the points (2, 4), (3, 1), (1, 0),(1,2) and (3,5)lie? Verify your answer by locating them on the Cartesian plane.
Each equation contains statements given in two columns which have to be matched. Statements (a,b,c,d) in column I have to be matched with Statements (p, q, r, s) in column II. If the correct match are ap,as,bq,br,cp,cq, and ds , then the correctly bubbled 4x4 matrix should be as follows: Figure Consider the lines represented by equation (x2+xy−x)x(x−y)=0, forming a triangle. Then match the following: Column I|Column II Orthocenter of triangle |p. (61,21) Circumcenter|q. (1(2+22),21) Centroid|r. (0,21) Incenter|s. (21,21)