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Pair of Straight Lines Test - 3

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Pair of Straight Lines Test - 3
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  • Question 1
    1 / -0

    The straight lines x + y = 0 , 3x - y – 4 = 0 , x + 3y – 4 = 0 form a triangle which is

    Solution

    The lines formed by these lines is right angled, triangle.

    Two lines are perpendicular to each other if the product od their slopes is -1

    Slope of the lines 3x - y – 4 = 0 , x + 3y – 4 = 0 are 3 and -1/3 respectively.

    The product of these slopes is -1

    Hence the lines3x - y – 4 = 0 , x + 3y – 4 = 0 are perpendicular to each other.

    Therefore the triangle formed by these lines is a right angled triangle.

     

  • Question 2
    1 / -0

    The equation of the straight line passing through the intersection of the lines x - 2y = 1 and x + 3y = 2, and parallel to 3x + 4y = 0 is

  • Question 3
    1 / -0

    The distance between the parallel lines given by (x + 7y)2 + 4√2 (x + 7y) − 42 = 0 is

  • Question 4
    1 / -0

    The extremities of diagonal of a parallelogram are the points (3, − 4) and (− 6, 5). If the third vertex is (− 2, 1), then the fourth vertex will be

  • Question 5
    1 / -0

    The distance of the point (α,β) from X axis is

    1. α

    2.|β|

    3.|α|

    4.none of these.

    Solution

    The distance of a  point from X axis is its y coordinate.

    Hence the distance of the point (α,β) from X axis  is |β|

     

  • Question 6
    1 / -0

    Slope of a line is not defined if the line is

    Solution

    Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.

     

  • Question 7
    1 / -0

    The image of the point (α,β) with respect to the line x = y is

  • Question 8
    1 / -0

    The following question has four choices out of which ONLY ONE is correct.

    Consider a line pair ax2 + 3xy - 2y2 - 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the x-axis.

    If the circle x2 + y2 - 4y + k = 0 is orthogonal with the circumcircle of the triangle ABC, find the value of k.

  • Question 9
    1 / -0

    The point which divides the joint of ( 1, 2 ) and ( 3,4 ) externally in the ratio 1 : 1 .

    Solution

    The point which divides the line in the ratio m:n externally is given by x =m(x2)−n(x1)/m−n

    Substituting the values we get,

    x = 1(3)−1(1)/1−1 which is undefined.

     

  • Question 10
    1 / -0

    Above x-axis, the equation of the common tangent to the circle (x - 3)2 + y2 = 9 and parabola y2 = 4x is

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