Problema Solution
Parabolas y=3x2 and y=−3x2+k intersect at points M and N that are in the first and the second quadrants respectively. Find k if length of the segment MN is 6.
Answer provided by our tutors
The intersecting points M and N for the parabolas y=3x^2 and y=−3x^2+k are:
Plug y=3x^2 into y=−3x^2+k:
y = - y + k
y = k/2
3x^2 = k/2
x^2 = k/6
M(-√(k/6), k/2) and N(√(k/6), k/2)
Since the segment has length of 6 we have:
2√(k/6) = 6
√(k/6) =3
k/6= 9
k = 9/6
k = 3/2
k = 1.5