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AP EAMCET202418 May 2024Morning ShiftMathematicsParabolaActual

If the axes are rotated through an angle 45^ about the origin in anticlockwise direction, then the transformed equation of y^2=4 a x is

Options

  1. A(x+y)^2=4 2 a(x-y)
  2. B(x-y)^2=4 2 a(x+y)
  3. C(x-y)^2= 4 a 2 (x+y)
  4. D(x+y)^2= 4 a 2 (x-y)

Correct answer

A. (x+y)^2=4 2 a(x-y)

Step-by-step solution

Given =45^ Let new co-ordinate be (x^ , y^ ) and old coordinate be (x, y) So, x=x^ 45^ -y^ 45^ = x^ -y^ 2 and y=x^ 45^ +y^ 45^ = x^ +y^ 2 Now, y^2=4 a x aligned & Now, y^2=4 ax & ( x^ +y^ 2 )^2=4 a ( x^ -y^ 2 ) (x^ +y^ )^2 & =4 a 2 (x^ -y^ ) aligned So, (x+y)^2=4 2 a(x-y)

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