Question 10.4.3: Relating the coordinates Suppose that the x- and y-axes are ...

Precalculus Functions and Graphs

Relating the coordinates

Suppose that the x– and y-axes are rotated through the angle π/3. If the point P has coordinates (2, 5) in the xy-system, then what are the coordinates of P in the x’y’-system?

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

This Question has been Answered.

Already have an account?

Related Answered Questions

Question: 10.4.6

Rotation of axes for an ellipse Use rotation of axes to write 21x² – 10√3xy + 31y² = 144 in the standard form of an ellipse and sketch its graph. ...

Verified Answer:

We have

A=21, B=-10 \sqrt{3}

, an...

Question: 10.4.5

Rotation of axes for a hyperbola Use rotation of axes to write y = 1/x in the standard form for a hyperbola. ...

Verified Answer:

Since y = 1/x is equivalent to xy - 1 = 0, we have...

Question: 10.3.3

Graphing a hyperbola centered at (h, k) Determine the foci and equations of the asymptotes, and sketch the graph of (x – 2)²/9 – (y + 1)²/4 = 1. ...

Verified Answer:

The graph that we seek is the graph of

\fr...

Question: 10.3.2

Graphing a hyperbola opening up and down Determine the foci and the equations of the asymptotes, and sketch the graph of 4y² – 9x² = 36. ...

Verified Answer:

Divide each side of the equation by 36 to get the ...

Question: 10.2.5

Finding the equation for a circle Write the equation for the circle that has center (4, 5) and passes through (-1, 2). ...

Verified Answer:

The radius is the distance from (4, 5) to (-1, 2):...

Question: 10.2.4

Graphing an ellipse centered at (h, k) Sketch the graph and identify the foci of the ellipse (x – 3)²/25 + (y + 1)²/9 = 1. ...

Verified Answer:

The graph of this equation is a translation of the...

Question: 10.2.2

Graphing an ellipse with foci on the x-axis Sketch the graph and identify the foci of the ellipse x²/9 + y²/4 = 1. ...

Verified Answer:

To sketch the ellipse, we find the x-intercepts an...

Question: 10.1.3

Finding the vertex, focus, and directrix Find the vertex, focus, and directrix of the parabola y = 2x² + 6x – 7 without completing the square, and determine whether the parabola opens upward or downward. ...

Verified Answer:

First use x = -b/(2a) to find the x-coordinate of ...

Question: 10.5.4

Converting a polar conic to rectangular coordinates Convert r = 4/2 – 2 sinθ to rectangular coordinates and identify the conic. Sketch the graph. ...

Verified Answer:

Convert to rectangular coordinates as follows: [la...

Question: 10.5.3

Finding the polar equation of a conic Find the equation of the conic that has its focus at the pole, directrix x = 3, and eccentricity 1. Graph it with a graphing calculator. ...

Verified Answer:

From the previous theorem we have e = 1, p = 3, an...