Maths-
General
Easy
Question
The ends of a line segment are P (1, 3) and Q (1, 1). R is a point on the line segment PQ such that PQ : QR = 1 : λ. If R is an interior point of the parabola y2 = 4x, then -
(0, 1)
-
- None of these
(0, 1)
Hint:
assume R to be (x,y) and find x and y in terms of lambda.
The correct answer is: (0, 1)
λ ε (0,1)
Let r = (x,y)
x= λ+1/λ+1
y= = 3λ+1/ λ+1
r lies inside parabola => y2<4x
(3λ+1/ λ+1)2 -4(λ+1/λ+1)<0
5 λ2-2 λ-3<0
This gives us λ ε (-3/5,1)
Since λ>0,
λ ε (0,1)
if a point lies inside the curve, then it gives a negative value when we substitute its value in the curve
zero when it lies on the curve and
positive value when it lies outside the curve.
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