Question

Which of the following statements are true and which are false? Give reasons for your
answer.
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 2x
2 +y
2 +3z
2 +4x+4y+18z+34 = 0,2x
2 −y
2 = 4y−4y−4x
represent a real conic.
vi) 4x
2 −9y
2 +z
2 +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

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Answer 1

Answer:

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