Engineering Board Exam Reviewer · Conic Sections and Transformation of Axes · medium

The coordinate axes are rotated counterclockwise through 90°. What are the new coordinates of the point (3,4)?

  1. (-4,3)
  2. (4,-3)
  3. (3,-4)
  4. (-3,4)

Answer

B. (4,-3)

Solution

x'=x +y =4 and y'=-x +y =-3 for =90°.

More Conic Sections and Transformation of Axes questions

  1. The axes are translated so that the first-degree terms of x2+y2-4x+6y-3=0 disappear. What is the new origin?
  2. Through what acute angle must the axes be rotated to eliminate the xy-term of x2-2 3,xy+3y2+4x=0? Give the answer in degrees.
  3. Identify the graph of 2x2+xy+3y2-5=0.
  4. Identify the graph of x2+4xy+4y2+3x-2=0.
  5. Identify the graph of x2+y2-4x+6y=3.
  6. A conic has a focus at (2,0), the directrix x=8, and eccentricity 12. Find its equation.
  7. The axes are rotated through 45°. Find the equation of xy=8 in terms of the new coordinates x' and y'.

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