Use a graphing utility to graph the conic.Determine the angle through which the axes are rotated.
A) ,
B) ,
C) ,
D) ,
E) ,

Question

Use a graphing utility to graph the conic.Determine the angle  through which the axes are rotated. ​  ​
A) , 
B) , 
C) , 
D) , 
E) ,

Quizplus · Accepted Answer

From the graph, we can see that the conic is an ellipse with major axis in the y-direction and minor axis in the x-direction. This means that the axes are rotated by some angle θ, where θ is the angle by which the positive y-axis must be rotated counterclockwise to align with the major axis of the ellipse.

To find θ, we can use the fact that the slope of the major axis is given by tan(θ) = b/a, where a is the length of the semi-major axis and b is the length of the semi-minor axis. From the graph, we can see that a = 4 and b = 1, so tan(θ) = 1/4.

Using a calculator, we can find that θ ≈ 14.04°. Therefore, the answer is C, 11eacce6_20b7_27c4_9f49_93ec0b57113e_TB7896_00 , 11eacce6_20b7_27c5_9f49_5b274c620b81_TB7896_00 11eacce6_20b7_27c6_9f49_0ddf4397c152_TB7896_00.

Use a Graphing Utility to Graph the Conic