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Standard XII

Mathematics

Area between x=g(y) and y Axis

Points A and ...

Question

Points A and B lie on the parabola $y = 2 x^{2} + 4 x - 2$ , such that origin is the mid-point of the line segment AB. If ‘l’ be the length of line segment AB, then find the unit digit of $l^{2}$ .___

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Solution

$β = 2 α^{2} + 4 α - 2$ ...(i)
$- β = 2 α^{2} - 4 α - 2$ ...(ii)
(i) & (ii) $\Rightarrow 4 α^{2} - 4 = 0 \Rightarrow α = \pm 1$
Put $α = 1, β = 2 + 4 - 2 = 4$
$t h e r e f o r e A (1, 4), B (- 1, - 4)$
$A B^{2} = l^{2} = (\sqrt{4 + 64})^{2} = 68$

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Points A and B lie on the parabola y=2x2+4x−2 , such that origin is the mid-point of the line segment AB. If ‘l’ be the length of line segment AB, then find the unit digit of l2.___

β=2α2+4α−2 ...(i) −β=2α2−4α−2 ...(ii) (i) & (ii) ⇒4α2−4=0⇒α=±1 Put α=1,β=2+4−2=4 thereforeA(1,4),B(−1,−4) AB2=l2=(√4+64)2=68

Points A and B lie on the parabola $y = 2 x^{2} + 4 x - 2$ , such that origin is the mid-point of the line segment AB. If ‘l’ be the length of line segment AB, then find the unit digit of $l^{2}$ .___

$β = 2 α^{2} + 4 α - 2$ ...(i)
$- β = 2 α^{2} - 4 α - 2$ ...(ii)
(i) & (ii) $\Rightarrow 4 α^{2} - 4 = 0 \Rightarrow α = \pm 1$
Put $α = 1, β = 2 + 4 - 2 = 4$
$t h e r e f o r e A (1, 4), B (- 1, - 4)$
$A B^{2} = l^{2} = (\sqrt{4 + 64})^{2} = 68$