Rotation of Axes
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The line L has intercepts a and b on the coordinate axes. When keeping the origin fixed, the coordinate axes are rotated through a fixed angle, then the same line has intercepts p and q on the rotated axes. Then
(I.I.T. 1990)
a2+b2=p2+q2
1a2+1b2=1p2+1q2
a2+b2=p2+q2
1a2+1p2=1b2+1q2
Final coordinates of a point as a result of rotating a point about origin through an angle of θ is equivalent to rotating the co-ordinate axes through an angle of −θ.
True
False
The origin of the co-ordinate axes is shifted to (-1, 3) and the axes is rotated through an angle of 90∘ in anti-clockwise direction. If (a, b) is the new coordinates of (2, 3) in the new coordinate system, then find the value of 2a2+3b2
The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p and q are the intercepts of the line L on the new axes, then 1a2−1p2+1b2−1q2 is equal to
0
1
none of these
-1
. Its equation if the axes are rotated through an angle 45° will be
- 2x2+y2=5
- 2x2+y2=10
- x2+2y2=5
- x2+2y2=10