Rotation of Axes
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Q. A line has intercepts a and b on the coordinate axes. When the axes are rotated through an angle α in anticlockwise direction, keeping the origin fixed, the line makes equal intercepts on the coordinate axes. Then the value of cotα is
- a+ba−b
- a−ba+b
- a2−b2
- a2+b2
Q. If the transformed equation of xy=c2 when the axis are rotated through an angle of π4 (in the anti clockwise direction), is pX2+qY2=rc2, then
- p=1
- p=−1
- q=1
- r=2
Q. If the axes are rotated through an angle of 90∘ in any direction then the transformed equation of x2=4ay can be
- Y2=4aX
- Y2=−4aX
- X2=4aY
- X2=−4aY
Q. The transformed equation of x2+6xy+8y2=10 when the axes are rotated through an angle π4 (in the anti clockwise direction) is aX2+2hXY+bY2=20 then which of the following is/are correct
- a+b=18
- h=14
- h=7
- a−b=12
Q. If the axes are shifted to (−2, −3) and then rotated through π4 in anticlockwise direction, then transformed equation of x2−y2+2x+4y=0 is
- 8x+12y−2√2xy−21√2=0
- 8x−12y−2√2xy−21√2=0
- 8x+12y+2√2xy−21√2=0
- 8x+12y+2√2xy+21√2=0
Q. The transformed equation of 3x2+3y2+2xy=2 when the coordinate axes are rotated through an angle 45∘ is
- X2+2Y2=1
- 2X2+Y2=1
- X2−2Y2=1
- 2X2−Y2=1
Q.
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
Q. The transformed equation of ax2+bxy+cy2=2 is 2X2+Y2=1, when the axes are rotated through an angle of 45∘ in anticlockwise direction. Then which of the following is (are) true?
- a2+b2+c2=20
- Roots of the equation am2+bm+c=0 are real
- Arithmetic mean of a and c is b+1
- Range of the function f(y)=ay−bby−c is R−{32}