Engineering Board Exam Reviewer · Conic Sections and Transformation of Axes · medium
The axes are translated so that the first-degree terms of x2+y2-4x+6y-3=0 disappear. What is the new origin?
- (2,-3)
- (-2,3)
- (4,-6)
- (2,3)
Answer
A. (2,-3)
Solution
Completing the squares gives (x-2)2+(y+3)2=16, so the new origin is the center (2,-3).
More Conic Sections and Transformation of Axes questions
- 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.
- Identify the graph of 2x2+xy+3y2-5=0.
- Identify the graph of x2+4xy+4y2+3x-2=0.
- Identify the graph of x2+y2-4x+6y=3.
- A conic has a focus at (2,0), the directrix x=8, and eccentricity 12. Find its equation.
- The axes are rotated through 45°. Find the equation of xy=8 in terms of the new coordinates x' and y'.
- The coordinate axes are rotated counterclockwise through 90°. What are the new coordinates of the point (3,4)?