Test Pair of lines 1) Find the combined equation of the lines passing through the origin and having inclinations and 2) Find the joint equation of the following pair of lines: 3) passing through (2, 3) and parallel to the co–ordinate axes. 4) Find the condition that the line 4x + 5y = 0 coincides with one of the lines given by ax2+ 2hxy + by2=0. 5) Find the joint equation of pair of lines through the origin and making an equilateral triangle with the line y=3. 6) If one of the lines given by ax2+2hxy + by2 = 0 bisects an angle between the co–ordinate axes, then show that (a + b)2 = 4h2. 7) Find the measure of acute angle between the lines represented by 3x2 –4 xy+3y2 = 0 8) Find the joint equation of pair of lines through the origin each of which making an angle of 30° with the line 3x+2y –11 = 0. 9) Find k if slope of one of the lines given by kx2 + 4xy –y2 = 0 exceeds the slope of the other by 8. 10) Find the separate equations of the lines represented by a) 5x2–3 y2 = 0 b ) x2 + 2(cosec α) xy + y2 = 0 11) Show that the equation x2- 6xy + 5 y2 + 10x - 14y + 9 = 0 represents a pair of lines. Find the acute angle between them. Also find the point of intersection of the lines. 12) Find p and q if the following equation represents a pair of perpendicular lines 2x2+4xy-py2+4x + qy+ 1=0. 13) If one of the lines given by ax2+ 2hxy + by2 = 0 is perpendicular to px + qy=0, show that ap2+2hpq + bq2=0. 14) If the angle between the lines represented by ax2+ 2hhxy + by2 = 0 is equal to the angle between line 2x2– 5xy+3y2= 0, then show that 100(h2–ab)=(a + b)2. 15) Find the separate equations of the lines represented by the following equations: 10(x+l)2+(x+l)(y–2)–3(y–2)2 = 0 16) Find the value of k, if the following equation represent a pair of lines 3x2+10xy+3y2+16y+k=0 Further find, whether these lines are parallel or intersecting ? 17) AOAB is formed by the lines x2 – 4xy + y2 = 0 and the line AB. The equation of line AB is 18) 2x + 3y – 1 = 0. Find the equation of the median of the triangle drawn from the origin. 19) Find the joint equation of a pair of lines which bisects angle between the lines given by x2 + 3xy+2y2=0. 20) If the lines represented by ax2 + 2hxy + by2 = 0 make angles of equal measures with the co-ordinate axes then show that a = ±b. 21) Find the combined equation of lines passing through the point P(l,2) and perpendicular to both the lines 3x+2y-5 = 0 and 2x-5y+1=0.