ParabolaEasy
Question
If the focus of the parabola (y - λ)2 = 4(x - λ) always lies between the lines 2x + y = 1 and 2x + y = 3 then the sum of all integral values of λ is -
Options
A.0
B.1
C.2
D.infinite
Solution
Focus of parabola is (λ + 1, λ)
∴ (2(λ + 1) + λ - 1). (λ + 1 + 2λ - 3) < 0
⇒ (3λ + 1)(3λ - 1) < 0 ⇒
∴ Integral value of λ is 0.
∴ (2(λ + 1) + λ - 1). (λ + 1 + 2λ - 3) < 0
⇒ (3λ + 1)(3λ - 1) < 0 ⇒
∴ Integral value of λ is 0.
Create a free account to view solution
View Solution FreeMore Parabola Questions
If two distinct chords of parabola $y^{2} = 4ax(a > 0)$ passing through $(a,2a)$ are bisected by the line $x + y = 1$...The points of contact $Q$ and $R$ of tangent from the point $P(2,3)$ on the parabola $y^{2} = 4x$ are:...If two distinct chords of a parabola $y^{2} = 4ax$ passing through the point $(a,2a)$ are bisected by line $x + y = 1$, ...The tangent PT and the normal PN to the parabola y2 = 4ax at a point P on it meet its axis at points T and N, respective...Let PQ be a double ordinate of the parabola, y2 = − 4x, where P lies in the second quadrant. If R divides PQ in th...