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The straight lines represented by (y - mx)2 = a2 (1 + m2 ) and (y - nx)2 = a2 (1 + n2 ) form a
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the lines can also be written as y - mx = (+-)[a.sqrt(1 + m2) ] and y - nx = (+-)[a.sqrt(1 + n2) ] if u know the condition of tangency these four lines represents the pairs of equation of angents to the circle of radius a hence two are parallel and other wo are also parallel hence the four lines represents the parabola (m is not equal to n) and represent the rhombus only when (m = 1 and n = -1) or (m = -1 and n = 1) hence in general lines represents parallelogram but not rhombus try to visualise it |
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