1969 AHSME Problems/Problem 21
Problem
If the graph of is tangent to that of , then:
Solution
Note that the first equation represents a circle and the second equation represents a line. If a line is tangent to a circle, then it only hits at one point, so there will only be one solution to the system of equations.
In the second equation, . Substitution results in In order for the system to have one solution, the discriminant must equal . Thus, can be a non-negative real number, so the answer is .
See Also
1969 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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