my teacher said anyone in my class who gets this question would get a prize in front of the whole school.... okay.... i exaggerate.... but still, i want to understand this.
the question is:
consider the circle x^2 + y^2 = 25 and the line y = x +k, where k is any real number. Determine the values of k for which the line will intersect the circle in one, two, or no points. Repeat for the circle x^2 + y^2 = 49 and the line y = x+k.
generalize your results for a circle of radius r and the line y = x+k
Note: the question asks for you to do two. Dont worry about it, just explain the steps and i will understand it.
Thanks in advance
Hello, thejoester!
Consider the circle and the line
Determine the values of for which the line will intersect the circle in 1, 2, or 0 points.
To complete what ThePerfectHacker started . . .
The discriminant is: .
To have one point of intersection,
. .
To have two points of intersection:
. .
To have no points of intersection:
. .
The "graph" looks like this:
. .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . .