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# Lecture - 14 Chapter 10 Straight Lines

MISCELLANEOUS EXERCISE |

**Question 8. **Find the area of the triangle formed by the lines *y* – *x* = 0, *x* + *y* = 0 and *x* – *k* = 0.

**Question 9. **Find the value of p so that the three lines 3*x* + *y* – 2 = 0, *px* + 2* y* – 3 = 0 and 2*x* – *y* – 3 = 0 may intersect at one point.

**Question 10. **If three lines whose equations are \( y=m_1x+c_1, y=m_2x+c_2 \text{ and } y=m_3x+c_3 \) are concurrent, then show that \( m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0\).

**Question 11. **Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line *x* – 2*y* = 3.

**Question 13. **Show that the equation of the line passing through the origin and making an angle θ with the line *y*=*mx*+*c* is \( \frac{y}{x} = \frac{(m \pm \tan \theta)} {(1 \mp m)} \).

**Question 12. **Find the equation of the line passing through the point of intersection of the lines 4*x* + 7*y* – 3 = 0 and 2*x* – 3*y* + 1 = 0 that has equal intercepts on the axes.