“The whole secret of a successful life is to find out what is one’s destiny to do, and then do it.” –Henry Ford

# Lecture - 17 Chapter 10 Straight Lines

**Miscellaneous Example 20. **If the lines 2*x*+*y*-3=0, 5*x*+*ky*-3=0 and 3*x*–*y*-2=0 are concurrent, find the value of *k*.

**Miscellaneous Example 21. **Find the distance of the line 4*x* – *y* = 0 from the point P (4, 1) measured along the line making an angle of 135° with the positive *x*-axis.

**Miscellaneous Example 22. **Assuming that straight lines work as the plane mirror for a point, find the image of the point (1, 2) in the line *x* – 3*y* + 4 = 0.

**Miscellaneous Example 23. **how that the area of the triangle formed by the lines \( y=m_1x+c_1, y=m_2x+c_2 \) and \( x=0 \) is \( \frac{(c_1-c_2)^2}{2|m_1-m_2|}\).

**Miscellaneous Example 24. **A line is such that its segment between the lines 5*x* – *y* + 4 = 0 and 3*x* + 4*y* – 4 = 0 is bisected at the point (1, 5). Obtain its equation.

**Miscellaneous Example 25. **Show that the path of a moving point such that its distances from two lines 3*x* – 2*y* = 5 and 3*x* + 2*y* = 5 are equal is a straight line.