JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q78

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MathematicsSingle correct+4 / -1Question 78 of 90

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

The line $\sqrt3x+y=1$ makes 120° with the $x$ -axis, so L makes 60° or 180°. A horizontal L through $(3,-2)$ never meets the $x$ -axis, so L has slope $\sqrt3$ :
$y+2=\sqrt3(x-3)\iff y-\sqrt3x+2+3\sqrt3=0.$

Topics:Angle between lines Equations of a line

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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 78