SOLUTION: Consider the circle x^2 + y^2 - 2x -14y +25=0
Show that, if the line y=mx intersects the circle in two distinct points, then (1+7m)^2 -25(1+m^2) > 0
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-> SOLUTION: Consider the circle x^2 + y^2 - 2x -14y +25=0
Show that, if the line y=mx intersects the circle in two distinct points, then (1+7m)^2 -25(1+m^2) > 0
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Question 1140359: Consider the circle x^2 + y^2 - 2x -14y +25=0
Show that, if the line y=mx intersects the circle in two distinct points, then (1+7m)^2 -25(1+m^2) > 0 Answer by ikleyn(52809) (Show Source):
Substitute y = mx into the given equation of the circle and combine common terms.
The condition that the straight line intersects the circle in two points is equivalent to the fact that
the obtained quadratic equation has two real roots.
In turn, it means that the discriminant of this quadratic equation is POSITIVE.
The condition that the discriminant is positive is exactly the inequality of your post.
