JEE Main & Advanced Mathematics Straight Line Question Bank

done Numerical Value Type Questions - Straight Lines and Pair of Straight Lines Total Questions - 15

• question_answer1)
  Let the equations of two sides of a triangle be \[3x-2y+6=0\] and \[4x+5y-20=0\]. If the orthocenter of this triangle is at \[(1,1)\] and the equation of its third side is \[ax+by+c=0,\] then \[a+b-c\] is
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• question_answer2)
  The vertices of a rectangle ABCD are \[A(-1,0),\]\[B(2,0),\] \[C(a,b)\] and \[D(-1,4)\]. Then the length of the diagonal AC is
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• question_answer3)
  The vertices of triangle are \[(6,0),\,(0,6)\] and \[(6,6)\] The distance between its circumcentre and centroid is
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• question_answer4)
  Two sides of a parallelogram are along the lines, \[x+y=3,\] and \[x-y+3=0\]. If its diagonals intersect at \[(2,4)\] and one of its vertex is \[(a,b)\] then \[a+b\] is
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• question_answer5)
  If the pair of straight lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\]and \[{{x}^{2}}-2qxy-{{y}^{2}}=0\] be such that each pair bisects the angle between the other pair, then \[pq+3\] is
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• question_answer6)
  If in a parallelogram ABDC, the coordinates of A, B and C are respectively \[(1,2),(3,4)\] and \[(2,5)\]. If the equation of the diagonal AD is \[ax+by+c=0,\] then \[a+b+c\] is
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• question_answer7)
  If one of the lines given by \[6{{x}^{2}}-xy+4c{{y}^{2}}=0\] is \[3x+4y=0,\] then \[c+3\] equals
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• question_answer8)
  Suppose that the points \[(h,k),\,\,(1,2)\] and \[(-3,4)\] lie on the line \[{{L}_{1}}\]. If a line \[{{L}_{2}}\] passing through the points \[(h,k)\] and \[(4,3)\] is perpendicular on \[{{L}_{1}},\] then \[k+h\] equal to
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• question_answer9)
  If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] is four times their product, then the value of c is
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• question_answer10)
  The number of possible straight lines, passing through (2, 3) and forming a triangle with coordinate axes, whose area is \[12\text{ }sq\]. units, is
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• question_answer11)
  Let \[A(2,-3)\] and \[B(-2,3)\] be vertices of a triangle ABC. If the centroid of this triangle moves on the line \[2x+3y=1\]. If the locus of the vertex C is the line \[ax+by=c,\] then \[\frac{b+c}{a}\] is
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• question_answer12)
  If the point dividing internally the line segment joining the points \[(a,b)\] and \[(5,7)\] in the ratio \[2:1\] be \[(4,6),\] then \[a.b\] is
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• question_answer13)
  If one of the lines of \[m{{y}^{2}}+(1-{{m}^{2}})xy-m{{x}^{2}}=0,\]\[m>0\] is a bisector of the angle between the lines \[xy=0,\] then m is
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• question_answer14)
  If the two lines \[x+(a-1)y=1\] and \[2x+{{a}^{2}}y=1\,(a\in R-\{0,1\})\] are perpendicular, then the distance of their point of intersection from the origin is \[\sqrt{\frac{p}{q}},\] then \[p.q\] is
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• question_answer15)
  The distance between parallel lines \[3x-4y+9=0\] and \[6x-8y-15=0\] is
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