How can you check if a line and a circle intersect? - Answers

Okay, so you simply plug the equation of the line into the equation of the circle.(The reason you do this is because whenever they intersect, their x and y values are equal)I'll give an example.Say, for instance, you want to know if y=x+1 (the line) intersects with x2+y2=4 (the circle)Plug in the x+1 for the y in the circle.So you now have:x2+(x+1)2=4(Make sure that you include the parenthesis!)x2+(x+1)(x+1)=4x2+x2+2x+1=42x2+2x+1=42x2+2x-3=0Then you will use part of the quadratic formula, which is:x=(-b±√(b2-4ac))/2aFor this problem, you're interested in what the value under the radical sign is.(b2-4ac)Plug in the numbers22-(4)(2)(-3)4-(-24)4+2428When you plug in the numbers for b2-4ac (known as the discriminant)If the final result is:Greater than 0 - you have 2 intersection pointsEqual to 0 - you have 1 intersection pointLess than 0 - they do not intersectSo, for your original question, if the discriminant ends up being equal to or greater than 0, then the line and the circle intersect.I hope that made sense.