JEE Maths - Straight Lines

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Question - 1

If three distinct points A, B, C are given in the 2-dimensional coordinate plane such that the ratio of the distance of each one of them from the point ( 1, 0) to the distance from (- 1, 0) is equal to \(\frac{1}{2}\), then the circumcentre of the triangle ABC is at the point ___________ .

  • A \(\left(\frac{5}{3}, 0\right) \)
  • B (0,0)
  • C \(\left(\frac{1}{3}, 0\right)\)
  • D (3,0)

Question - 2

Let A (-3, 2) and B (-2, l) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line 3x + 4y + 2 = 0, then the vertex C lies on the line ___________ .

  • A 4x+3y+5=0
  • B 3x+4y+3=0
  • C 4x+3y+3=0
  • D 3x+ 4y+5=0

Question - 3

The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points \(\left(a^{2}+1, a^{2}+1\right)\) and \((2 \mathrm{a},-2 \mathrm{a}), \mathrm{a} \neq 0\). Then for any a, the orthocentre of this triangle lies on the line ___________ .

  • A y-2ax = 0
  • B \(y-\left(a^{2}+1\right) x=0 \)
  • C y + x = 0
  • D \((a-1)^{2} x-(a+1)^{2} y=0\)

Question - 4

The line parallel to the x- aris and passing through the intersection of the lines ax + 2by + 3b = 0 and \(b x-2 a y-3 a=0 \text {, where }(a, b) \neq(0,0) \text { is }\)____________ .

  • A below the x - aris at a distance of \( \frac{3}{2} \) from it
  • B below the x - aris at a distance of \(\frac{2}{3}\) from it
  • C above the x - axis at a distance of \( \frac{3}{2} \) from it
  • D above the x - axis at a distance of \(\frac{2}{3}\) from it

Question - 5

The straight line y = x - 2 rotates about a point where it cuts the x-axis and becomes perpendicular to the straight line ax + by + c = 0. Then its equation is ____________ .

  • A ax+by+2a=0
  • B ax-by-2a=0
  • C bx+ay-2b=0
  • D ay-bx+2b = 0

Question - 6

If the point (a,2) lies between the lines x - y - 1 = 0 and 2 (x-y) + 5 = 0, then the set of values of 'a' is _____________ .

  • A \((-\infty, 3) \cup\left(\frac{9}{2}, \infty\right) \)
  • B \(\left(3, \frac{9}{2}\right) \)
  • C \((-\infty, 3) \)
  • D \(\left(-\frac{1}{2}, 3\right)\)

Question - 7

If two vertices of a triangle are (5, -1) and (-2,3) and its orthocentre is at (0, 0), then the third vertex is ____________ .

  • A (4, -7)
  • B (-4, -7)
  • C (-4,7)
  • D (4, 7)

Question - 8

The base of an equilateral triangle is along the line given by 3x+4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is __________ .

  • A \(\frac{2 \sqrt{3}}{15} \)
  • B \(\frac{4 \sqrt{3}}{15} \)
  • C \(\frac{4 \sqrt{3}}{5} \)
  • D \(\frac{2 \sqrt{3}}{5}\)

Question - 9

The equation of bisector of that angle between the lines x + y + 1 = 0 and 2x -3y- 5 = 0 which contains the point (10, -20) is ___________ .

  • A \(x(\sqrt{13}+2 \sqrt{2})+y(\sqrt{13}-3 \sqrt{2})+(\sqrt{13}-5 \sqrt{2})=0 \)
  • B \(x(\sqrt{13}-2 \sqrt{2})+y(\sqrt{13}+3 \sqrt{2})+(\sqrt{13}+5 \sqrt{2})=0 \)
  • C \(x(\sqrt{13}+2 \sqrt{2})+y(\sqrt{13}+3 \sqrt{2})+(\sqrt{13}+5 \sqrt{2})=0\)
  • D None of these

Question - 10

The bisector of the acute angle formed between the lines 4x-3y+7 = 0 and 3x-4y+14 = 0 has the equation __________ .

  • A x+y+3=0
  • B x-y-3=0
  • C x-y-3=0
  • D 3x+y-7=0
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