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QJEEM21Ma8c74: JEE Main 2021 Mathematics - Class 11 JEEM21Ma8c74 Solution: Let A be the set of all points ( , ) such that the area of…

Let A be the set of all points ( α\alpha , β\beta ) such that the area of triangle formed by the points (5, 6), (3, 2) and ( α\alpha , β\beta ) is 12 square units. Then the least possible length of a line segment joining the origin to a point in A, is :

Multiple Choice Options

  • A 45{4 \over {\sqrt 5 }}
  • B 165{16 \over {\sqrt 5 }}
  • C 85{8 \over {\sqrt 5 }}
  • D 125{12 \over {\sqrt 5 }}

Step-by-Step Verified Solution

JEE Main 2021 (Online) 31st August Evening Shift Mathematics - Straight Lines and Pair of Straight Lines Question 64 English Explanation

|12|561321αβ1||=12

4 α\alpha −- 2 β\beta = ±\pm 24 + 8

⇒\Rightarrow 4 α\alpha −- 2 β\beta = + 24 + 8 ⇒\Rightarrow 2 α\alpha −- β\beta = 16

2x −- y −- 16 = 0 ..... (1)

⇒\Rightarrow 4 α\alpha −- 2 β\beta = −- 24 + 8 ⇒\Rightarrow 2 α\alpha −- β\beta = −- 8

2x −- y + 8 = 0 ...... (2)

Perpendicular distance of (1) from (0, 0)

∣0−0−165∣=165\left| {{{0 - 0 - 16} \over {\sqrt 5 }}} \right| = {{16} \over {\sqrt 5 }}

Perpendicular distance of (2) from (0, 0)

∣0−0+85∣=85\left| {{{0 - 0 + 8} \over {\sqrt 5 }}} \right| = {8 \over {\sqrt 5 }}

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