As you can see in the picture , two equations have been combined using the symbol lambda 1.Using what logic has that been done?2. Can we use the same logic too solve all types of equations?

As you can see in the picture , two equations have been combined using the symbol lambda 1.Using what logic has that been done?2. Can we use the same logic too solve all types of equations? S the Set a" gossible values of parameter a • fcy which the purrs intersectur ct parab&as Sax ar•d y — ( x: • ax 5 are curycbc_ Ttpn S contaaas jrrervaj(s) F of curves passing the pents ot intersection of parabolas is represents a circle it A it rv-vvosonts a mai circle if a: 1 — S O a: • a -2) e (2. x). Hence (A1 and (O) are the correct answers.

Dear Student,

The λ symbol is used here in the below equation to depict the equation of family of curvesIn the given question it represent the family of parabola which contains two given parabolasy2=3ax and y=12x2+ax+5since these parabolas intersect and there point of intersection should be concyclic i.e they should liw on a circleHence this family of curves should represent a circle.For answer to second question yes this logic is used to find family of curves and can be used to solve equations where  we need to find equation of family of curvesbut can not be used in any other cases.

Regards,

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