Question

Which of the following statements are true and which are false? Give reasons for your answer. (20) i) The equation r = acos(θ +α)+bsin(θ +α) represents a circle. ii) The direction ratios of the line x−5 = 5−y,z = 5 are 1,1,5. iii) The intersection of a plane and a cone can be a pair of lines. iv) The angle between the planes x+2y+2z = 5 and 2x+2y+3 = 0 is 60◦. v) The equations 2x2+y2+3z2+4x+4y+18z+34 = 0,2x2−y2 = 4y−4y−4x represent a real conic. vi) 4x2−9y2+z2+36 = 0 represents a hyperboloid of one sheet. vii) The intersection of any plane with an ellipsoid is an ellipse. viii) No plane passes through the points (1,2,3),(1,−1,0) and (1,1,2). ix) The circle with centre (a,0) and radius a, where a > 0, touches all the sides of the square x = 0,x = a,y =±a. x) If the projection of a line segment AB on a line L is 0, then AB lies in L.

Answer 1

20 Step-by-step explanation:

well i just guessed but