The lines y=x2 + 3x -1 and y = 2x + 5 intersect at 2 points. The line joining the two points has the length ksqrt(5). Find the value of k.
Hint - use Pythagoras' theorem to find the distance between the two points
+129657 y=x^2 + 3x -1 and y = 2x + 5 intersect at 2 points. The line joining the two points has the length ksqrt(5). Find the value of k.
Let's find the intersection points....set the functions equal
x^2 + 3x - 1 = 2x + 5 subtract the right side from the left
x^2 + x - 6 = 0 factor
(x - 3)(x +2) = 0 setting both factors to 0, the x coordinates of the intersection points are 3 and - 2
And using y = 2x + 5, the y intersection points are 2(3) + 5 = 11 and 2(-2) + 5 = 1
So....the intersection points are (3, 11) and ( -2, 1)
The distance between these = √ [ -2-3)^2 + (11 - 1)^2 ] = √ [ (-5)^2 + (10)^2 ] = √ [ 25 + 100] = √125 = √ [ 25 * 5] = √25 *√ 5 = 5 √ 5
So.....k = 5
