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1) Show that the combine equation of pair of lines passing through the origin is a, homogeneous equation of degree 2 in x and y. Hence find the combined, equation of the lines 2x+3y=0 and x-2y=0, , 2) Show that the homogeneous equation of degree 2 in x and y represents a pair of, lines passing through the origin if h? — ab > 0, , 3) If @ is the acute angle between the lines given by ax? + 2hxy + by? =0, 2vh?—ab, , Re, a+b, , , , , , then prove that tan 9 = Hence find acute angle between the lines, , 2x? + 7xy + 3y? =0, 4) If the angle between the lines represented by ax? + 2hxy + by? =0, , is equal to the angle between the lines 2x? — 5xy + 3y? = 0. then show that, 100(h? — ab) = (a+b)?