JEE Main & Advanced Mathematics Straight Line Question Bank

done Numerical Value Type Questions - Point Total Questions - 15

• question_answer1)
  A point P moves in such a way that sum of its perpendicular distances from two perpendicular lines in its plane is always 2. Then find the area of region bounded by locus of P.
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• question_answer2)
  Point Q is symmetric to P (4, -1) with respect to the bisector of the first quadrant. If length of PQ is \[k\sqrt{2}\]then find k.
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• question_answer3)
  If the extremities of the base of an isosceles triangle are the points \[(2a,0)\] and \[(0,a)\] and the equation of one of the sides is \[x=2a\]. If the area of the triangle is \[k{{a}^{2}}\] sq. units then find k.
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• question_answer4)
  If length of the median from B on AC, where \[A\left( -1,\text{ }3 \right),\text{ }B\left( 1,\text{ }-1 \right),\text{ }C\left( 5,\text{ }1 \right)\] is \[\sqrt{k}\] then find k.
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• question_answer5)
  If the area of the triangle with vertices\[(x,0),(1,1)\]and (0, 2) is 4 sq unit, then find the value of x.
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• question_answer6)
  If orthocenter and circumcentre of triangle are respectively (1, 1) and (3, 2) and the coordinates of its centroid are (h, k) then find \[h\text{ }+\text{ }k.\]
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• question_answer7)
  Find the area of quadrilateral formed by the lines\[3\left| \,\,x\,\, \right|+4\left| y \right|=6\].
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• question_answer8)
  Find the area of triangle formed by the lines \[xy\text{ }=\text{ }0\] and \[x+y=4.\]
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• question_answer9)
  If (2, 3), (-1, 10) and (4, 5) are the vertices of a triangle then find the square of distance between circum center and orthocenter.
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• question_answer10)
  The centroid of a triangle is (1, 4) and the coordinates of its two vertices are (4, - 3) and (- 9, 7). Then find the area of the triangle.
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• question_answer11)
  \[\left( {{x}_{i}},{{y}_{i}} \right)\]are vertices of a equilateral triangle ABC such that \[{{\left( {{x}_{1}}-2 \right)}^{2}}+{{\left( {{y}_{1}}-3 \right)}^{2}}={{\left( {{x}_{2}}-2 \right)}^{2}}+{{\left( {{y}_{2}}-3 \right)}^{2}}\] \[={{\left( {{x}_{3}}-2 \right)}^{2}}+{{\left( {{y}_{3}}-3 \right)}^{2}}\].Then \[2\left( {{x}_{1}}+{{x}_{2}}+{{x}_{3}} \right)+3\left( {{y}_{1}}+{{y}_{2}}+{{y}_{3}} \right)=\]
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• question_answer12)
  Opposite vertex of a square are (-1, 2) and (3, 4) then find the area of square.
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• question_answer13)
  Mid-point of sides of a triangle in x-y plane are\[\left( 1,\text{ }1 \right),\text{ }\left( 4,\text{ }3 \right)\text{ }\And \text{ }\left( 3,\text{ }5 \right)\]. Then find area of triangle.
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• question_answer14)
  If the incentre of triangle formed by coordinates axes and line \[3x+4y=12\] is \[\left( a,b \right)\] then find the value of  \[9a+8b\].
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• question_answer15)
  If the vertices of a quadrilateral is given by \[{{\left( {{x}^{2}}-9 \right)}^{2}}+{{\left( {{y}^{2}}-4 \right)}^{2}}=0\] and area of quadrilateral is \[\lambda \] then find the value of \[\lambda /3\].
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