The normal chord at a variable point on a hyperbola cuts the principal axes inP,Q . Prove that the locus of the mid-points of PQ is a hyperbola. Can it COincide with the original hyperbola?
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Answer: Yes it can.
In maths, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. It has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone.
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