Conic Sections Ncert Solutions Maths class 11th Maths Class 11th

If two distinct chords of a parabola y² = 4ax passing through (a, 2a) are bisected on the line x + y = 1, then the sum of integral values of the length of possible latus rectums is equal to

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Answered by

alok kumar singh | Contributor-Level 10

3 weeks ago

Any point on x + y = 1 can be taken as (t, 1 – t) The equation of chord with this as mid-point is y (1 – t) -2a (x + t) = (1 – t)² – 4at

It passes through (a, 2a)

So, t² – 2t + 2a² – 2a + 1 = 0

This should have two distinct real roots.

So D > 0

$\begin{array}{l} \Rightarrow a^{2} - a < 0 \\ \Rightarrow 0 < a < 1 \end{array}$

So, length of latus rectum < 4 and 0 < a < 1

$\Rightarrow L R = 1, 2, 3$

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...more

Slope of axis = $\frac{1}{2}$

$y - 3 = \frac{1}{2} (x - 2)$

⇒ 2y – 6 = x – 2

⇒ 2y – x – 4 = 0

2x + y – 6 = 0

4x + 2y – 12 = 0

α + 1.6 = 4 ⇒ α = 2.4

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Ellipse passes through (2.4, 3.2)

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$\frac{a^{2}}{b^{2}} = \frac{1}{2}$

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$\frac{144}{25} + \frac{256}{25} \times \frac{1}{2} = a^{2}$

$\frac{(128 + 144)}{25} = a^{2} \Rightarrow \frac{272}{25} = a^{2}$

-> $b^{2} = \frac{2 \times 272}{25}$

Latus rectum = $\frac{2 b^{2}}{a}$

(Latus rectum)²

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less

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48 = 16 (e2 – 1)

$e = \sqrt[]{4} = 2$

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If two distinct chords of a parabola y² = 4ax passing through (a, 2a) are bisected on the line x + y = 1, then the sum of integral values of the length of possible latus rectums is equal to

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If two distinct chords of a parabola y2 = 4ax passing through (a, 2a) are bisected on the line x + y = 1, then the sum of integral values of the length of possible latus rectums is equal to

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If two distinct chords of a parabola y² = 4ax passing through (a, 2a) are bisected on the line x + y = 1, then the sum of integral values of the length of possible latus rectums is equal to