Pair of Straight Line
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Questions and Answers

What is the joint equation of two lines a'x + b'y + c' = 0 and a''x + b''y + c'' = 0?

  • (a'x + b'y + c'') + (a''x + b''y + c'') = 0
  • (a'x + b'y + c'') / (a''x + b''y + c'') = 0
  • (a'x + b'y + c')(a''x + b''y + c'') = 0 (correct)
  • (a'x + b'y + c'') - (a''x + b''y + c'') = 0

    • What is the equation of a pair of straight lines passing through the origin?

  • ax^2 - 2hxy - by^2 = 0
  • ax^2 - 2hxy + by^2 = 0
  • ax^2 + 2hxy + by^2 = 0 (correct)
  • ax^2 + 2hxy - by^2 = 0

    • If m1 and m2 are the slopes of two lines represented by ax^2 + 2hxy + by^2 = 0, what is the relation between m1 and m2?

  • m1 + m2 = h/a
  • m1 + m2 = 1
  • m1 + m2 = -h/a (correct)
  • m1 + m2 = 0

    • What is the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be real and distinct?

    <p>h^2 - ab &gt; 0</p> Signup and view all the answers

    What is the condition for two pairs of lines ax^2 + 2hxy + by^2 = 0 and a'x^2 + 2h'xy + b'y^2 = 0 to have one line common?

    <p>(ab' - a'b)^2 = (ah' - a'h)(hb' - h'b)</p> Signup and view all the answers

    What is the equation of the pair of straight lines passing through the origin and perpendicular to the pair of straight lines represented by ax^2 + 2hxy + by^2 = 0?

    <p>bx^2 - 2hxy + ay^2 = 0</p> Signup and view all the answers

    What is the condition for the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 to represent a pair of straight lines?

    <p>abc + 2fgh - af - bg - ch = 0</p> Signup and view all the answers

    If the distance of two lines passing through the origin from the point (x1, y1) is d, then the equation of the lines is

    <p>(x1y - y1x)^2 = d^2(x1^2 + y1^2)</p> Signup and view all the answers

    What is the next step after factorizing the homogeneous part of the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0?

    <p>Add constants to the factors obtained</p> Signup and view all the answers

    The product of the perpendiculars drawn from (x1, y1) on the lines ax^2 + 2hxy + by^2 = 0 is given by

    <p>ax1^2 + 2hx1y1 + by1^2</p> Signup and view all the answers

    If the lines represented by the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 are perpendicular, then

    <p>f^2 + g^2 = h^2 - b^2</p> Signup and view all the answers

    What is the relationship between the slopes of the lines represented by the equation ax^2 + 2hxy + by^2 = 0 if one slope is the square of the other?

    <p>a^2b + ab^2 - 6abh + 8h^3 = 0</p> Signup and view all the answers

    The area of the triangle formed by the lines ax^2 + 2hxy + by^2 = 0 and lx + my + n = 0 is given by

    <p>1/2 |n^2(h^2 - ab) - am^2 - 2hlm + bl^2|</p> Signup and view all the answers

    What is the general equation of second degree in x and y?

    <p>ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0</p> Signup and view all the answers

    The orthocentre of the triangle formed by the lines xy = 0 and x + y = 1 is

    <p>(1/3, 1/3)</p> Signup and view all the answers

    If the lines represented by the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 are equidistant from the origin, what is the condition?

    <p>f^4 - g^4 = c(bf^2 - ag^2)</p> Signup and view all the answers

    What is the equation of the lines passing through the origin and perpendicular to the pair of straight lines represented by ax^2 + 2hxy + by^2 = 0?

    <p>ax^2 - 2hxy + by^2 = 0</p> Signup and view all the answers

    What is the square of the distance between the point of intersection of the lines represented by the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 and the origin?

    <p>f^2 + g^2 + h^2</p> Signup and view all the answers

    If the lines represented by the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 are perpendicular, what is the condition?

    <p>f^2 + g^2 = h^2</p> Signup and view all the answers

    What is the product of the perpendiculars drawn from the origin on the lines represented by the equation ax^2 + 2hxy + by^2 = 0?

    <p>c(a - b)^2 + 4h^2</p> Signup and view all the answers

    If the lines represented by the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 are concurrent, then what is the value of fg?

    <p>ch</p> Signup and view all the answers

    What is the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to form an isosceles triangle?

    <p>a^2 = 3b^2</p> Signup and view all the answers

    If the equation hxy + gx + fy + c = 0 represents a pair of straight lines, then what is the value of fg?

    <p>ch</p> Signup and view all the answers

    What is the condition for the lines joining the origin to the points of intersection of line y = mx + c and the circle x^2 + y^2 = a^2 to be mutually perpendicular?

    <p>a^2(m^2 + 1) = 2c^2</p> Signup and view all the answers

    What is the area of the triangle formed by the lines ax^2 + 2hxy + by^2 = 0 and lx + my + n = 0?

    <p>(hn^2 - abm^2 - 2hlm + bl^2) / (8|h|)</p> Signup and view all the answers

    If the equation of a pair of straight lines is aX² + 2hXY + bY² = 0, what is the condition for the pair of straight lines to be perpendicular?

    <p>h² = -ab</p> Signup and view all the answers

    What is the equation of a pair of straight lines passing through the origin?

    <p>ax² + 2hxy + by² = 0</p> Signup and view all the answers

    What is the orthocentre of a triangle formed by the lines xy = 0 and x + y = 1?

    <p>(1, -1)</p> Signup and view all the answers

    What is the condition for the lines represented by ax² + 2hxy + by² = 0 to be real and distinct?

    <p>h² &gt; ab</p> Signup and view all the answers

    What is the relationship between the slopes of the lines represented by the equation ax² + 2hxy + by² = 0?

    <p>m₁m₂ = ab</p> Signup and view all the answers

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