Straight Lines · JEE Main previous year questions

2018 3 questions

1. Q152018 · 16 Apr 2018 · Shift 1

   The locus of the point of intersection of the lines, $\sqrt{2}x-y+4\sqrt{2}k=0$ and $\sqrt{2}kx+ky-4\sqrt{2}=0$ (k is any non-zero real parameter), is :

   1. A.an ellipse whose eccentricity is $\frac{1}{\sqrt{3}}$.
   2. B.an ellipse with length of its major axis $8\sqrt{2}$.
   3. C.a hyperbola whose eccentricity is $\sqrt{3}$.
   4. D.a hyperbola with length of its transverse axis $8\sqrt{2}$.
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   Answer: D

2. Q182018 · 16 Apr 2018 · Shift 1

   If the angle between the lines, $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\frac{5-x}{-2}=\frac{7y-14}{p}=\frac{z-3}{4}$ is ${\cos }^{-1}\left(\frac{2}{3}\right)$, then p is equal to :

   1. A.$\frac{7}{2}$
   2. B.$\frac{2}{7}$
   3. C.$-\frac{7}{4}$
   4. D.$-\frac{4}{7}$
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   Answer: A

3. Q152018 · 8 Apr 2018 · Shift 1

   A straight line through a fixed point (2, 3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is :

   1. A.3x + 2y = 6xy
   2. B.3x + 2y = 6
   3. C.2x + 3y = xy
   4. D.3x + 2y = xy
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   Answer: D