Find the range of values of k such that the circle $x ^{2}+y ^{2}+2x-4y-13=0$ and the straight line x-y+k=0 intersect at two distinct points. A. -93 D. k9 @Callisto @appleduardo

Question

Find the range of values of k such that the circle $x ^{2}+y ^{2}+2x-4y-13=0$ and the straight line x-y+k=0 intersect at two distinct points. A. -93 D. k<-3 or k>9 @Callisto @appleduardo

callisto · Answer

x = y-k <-  Sub this into the equation of circle, you'll have an quadratic equation. 2 distinct intersections implies delta > 0, then you can solve for the range of k.

callisto · Answer

Maybe it's better to sub y=x+k...

anonymous · Answer

my final step is like this$$2y ^{2}-2y-2ky+k ^{2}-2k-13=0$$
what's wrong with this step?? :O

anonymous · Answer

you know the slope of the given line 
this line can be at a max. of radius of given circle

anonymous · Answer

max. distance is from center

callisto · Answer

Can be, but how can you be sure?

anonymous · Answer

because lines makes two intercept with given circle

anonymous · Answer

@Callisto i got it -3<k<9 ?

anonymous · Answer

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