IIT-JEE 2011 · Paper 1 · Mathematics Q53

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MathematicsSingle correct+3 / -1Question 53 of 69

A straight line $L$ through the point $(3,-2)$ is inclined at an angle 60° to the line $\sqrt3x+y=1$ . If $L$ also intersects the $x$ -axis, then the equation of $L$ is

y+\sqrt3x+2-3\sqrt3=0

y-\sqrt3x+2+3\sqrt3=0

\sqrt3y-x+3+2\sqrt3=0

\sqrt3y+x-3+2\sqrt3=0

Answer and worked solution

Official answer: B

Directions. $\sqrt3x+y=1$ makes 120° with the x-axis. A line at 60° to it makes 60° or 180° with the x-axis.

Choice. The horizontal line $y=-2$ never meets the x-axis, so the slope is $\tan60°=\sqrt3$ :
$y+2=\sqrt3(x-3)\iff y-\sqrt3x+2+3\sqrt3=0.$

(B)

Topics:Angle between lines Equations of a line

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IIT-JEE 2011 · Paper 1, Mathematics question 53