NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Let 2 a + 2 b + c = 0 , then the equation of the straight line a x + b y + c = 0 which is farthest from the point 1,1 is

Options

Ay = x
By + x = 2
Cy + x = 4
Dy = x + 2

Correct answer

C. y + x = 4

Step-by-step solution

All the lines a x + b y + c = 0 pass through the point 2,2 . The line passing through 2,2 & farthest from 1,1 is perpendicular to the line joining 1,1 & 2,2 Now, the slope of the line joining 1,1 & 2,2 is 2 - 1 2 - 1 = 1 ⇒ The slope of the required line is - 1 ⇒ Required line is y - 2 x - 2 = - 1 ⇒ y + x = 4

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