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

Identify the graph of x2+y2-4x+6y=3.

  1. Circle
  2. Ellipse
  3. Parabola
  4. Hyperbola

Answer

A. Circle

Solution

The x2 and y2 coefficients are equal and there is no xy term, so the graph is a circle: (x-2)2+(y+3)2=16.

More Conic Sections and Transformation of Axes questions

  1. A conic has a focus at (2,0), the directrix x=8, and eccentricity 12. Find its equation.
  2. The axes are rotated through 45°. Find the equation of xy=8 in terms of the new coordinates x' and y'.
  3. The coordinate axes are rotated counterclockwise through 90°. What are the new coordinates of the point (3,4)?
  4. The axes are translated so that the first-degree terms of x2+y2-4x+6y-3=0 disappear. What is the new origin?
  5. 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.
  6. Identify the graph of 2x2+xy+3y2-5=0.
  7. Identify the graph of x2+4xy+4y2+3x-2=0.

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