1. Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is (a) Parallel to the x-axis,
(b) Parallel to the y-axis,
(c) Passing through the origin.
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2. Find the values of θ and p, if the equation x cos θ + y sinθ = p is the normal form ... | |

3. Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively. | |

4. What are the points on the y-axis whose distance from the line
is ... 4 units. | |

5. Find perpendicular distance from the origin of the line joining the points (cosθ, sin θ)
and (cos φ, sin φ). | |

6. Find the equation of the line parallel to y-axis and drawn through the point ofintersection of the lines x – 7y + 5 = 0 and 3x + y = 0. | |

7. Find the equation of a line drawn perpendicular to the line ... through the point, where it meets the y-axis. | |

8. Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.
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9. Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
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10. If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m
are concurrent, then show that ... | |

11. Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line x – 2y = 3.
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12. Find the equation of the line passing through the point of intersection of the lines
4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes | |

13. Show that the equation of the line passing through the origin and making an angle θ with the line ... | |

14. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?
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15. Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x – y = 0.
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16. Find the direction in which a straight line must be drawn through the point (–1, 2)
so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point. | |

17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find the equation of the legs (perpendicular sides) of the triangle. | |

18. Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the
line to be a plane mirror. | |

23. Prove that the product of the lengths of the perpendiculars drawn from the ... | |

24. A person standing at the junction (crossing) of two straight paths represented by
the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose
equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he
should follow. | |