A system asks for a point that works in two equations at once. For a circle and a horizontal line, graph both equations as written in Desmos and click their intersections. Each intersection satisfies both equations. If you need , read the first coordinate, not the given -value or the circle’s farthest edge.
Hints
- Hint 1
An intersection is a point where two graphs meet, so its coordinates work in both equations. Enter the circle equation and the line equation on separate Desmos lines. Where do they cross?
- Hint 2
A horizontal line such as fixes the second coordinate of every point on it. Click each crossing with the circle, then look at the first coordinate for .
Step-by-step
Approach 1: Graph both equations
Step 1Find where the graphs cross
Type and on separate Desmos lines. The first draws a circle, and the second draws a horizontal line. They cross twice; each intersection is a point on both graphs.
- Step 2
Read the requested coordinate
Click both crossings. Desmos labels them and . In a point written , is the first coordinate. So one possible value of is ; is the given -value. Choice D.
Approach 2: Substitute the fixed coordinate
Step 1Use the given value of y
Use substitution: because the line fixes at , replace with in the circle equation. This makes an equation for alone:
- Step 2
Isolate the square
Square :
Subtract from both sides:
- Step 3
Keep both signs
Both and square to , so keep both square roots:
The question asks for one possible , so works. Choice D.