Circle And System Of Circles Question 324
Question: If $ c^{2}>a^{2}(1+m^{2}), $ then the line $ y=mx+c $ will intersect the circle $ x^{2}+y^{2}=a^{2} $
Options:
A) At one point in time
B) At two distinct points in time
C) At no point in time
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
If $ c^{2}<a^{2}(1+m^{2}) $, then line $ y=mx+c $ intersects the circle $ x^{2}+y y^{2}=a^{2} $ in two points; if $ c^{2}=a^{2}(1+m^{2}) $, then it intersects at one point; if $ c^{2}>a^{2}(1+m^{2}) $, then it intersects at no point.
BETA
