Questions: If the figure below is rotated 90 degrees counter-clockwise, what is the radius of the circle that has a center at (0,0) and intersects both F and F'?

If the figure below is rotated 90 degrees counter-clockwise, what is the radius of the circle that has a center at (0,0) and intersects both F and F'?

Transcript text: If the figure below is rotated 90 degrees counter-clockwise, what is the radius of the circle that has a center at $(0,0)$ and intersects both F and F'?

Solution

Solution Steps

Step 1: Identify the coordinates of point F

Point F is located at (5, 0).

Step 2: Rotate point F 90 degrees counter-clockwise

To rotate a point (x, y) 90 degrees counter-clockwise around the origin, the new coordinates will be (-y, x). Therefore, the coordinates of F' after rotation will be (0, 5).

Step 3: Calculate the radius of the circle

The radius of the circle is the distance from the center (0, 0) to either point F or F'. Both points are 5 units away from the origin.