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

B) At two distinct points

C) At no point

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

If $ c^{2}< $ or = or $ >a^{2}(1+m^{2}) $ , then line $ y=mx+c $ intersects the circle $ x^{2}+y^{2}=a^{2} $ in two points, a point or no point. Here intersect at no point.