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Lecture - 14 Chapter 10 Straight Lines

MISCELLANEOUS EXERCISE

Question 8. Find the area of the triangle formed by the lines yx = 0, x + y = 0 and xk = 0.

Question 9. Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and 2xy – 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 – 2y = 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 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

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