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Consider the quadratic trinomial function y=ax^(2)+bx+c,ane0,a,b,cinR. We know that on rectangular cartesian coordinate system the above equation represents a parabola, whose axis is parallel to axis of y. The characteristics of this parabola can be further analysed by rewriting the equation as following: y=a(x+b/(2a))^(2)+((4ac-b^(2))/(4a)). So, the vertex of the parabola is (-b/(2a),(4ac-b^(2))/(4a)). Focus of the parabola is (-b/(2a),(4ac-b^(2)+1)/(4a)). Latus rectum of the parabola is 1/|a| Holding one or two of the parameters a, b, c constant we can find family of parabolas satisfying some very significant properties. If b and c are constant but a varies from member to member, then the parabolas of the family

Answer»

have COMMON directrix
have common axis
touch a common line at a FIXED point
are equal parabolas

Answer :C


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