Constructing a transformation satisfying the given propertiesConstruct a transformation which maps the plane into the plane itself , and the curve y=x2 onto the horizontal axis, and the line y=3 onto the vertical axis.I need to solve the set of equationsT(x,x2)=(x,0)T(x,3)=(0,y)but couldn't. Any hints?

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Constructing a transformation satisfying the given propertiesConstruct a transformation which maps the plane into the plane itself , and the curve y=x2 onto the horizontal axis, and the line y=3 onto the vertical axis.I need to solve the set of equationsT(x,x2)=(x,0)T(x,3)=(0,y)but couldn&#039;t. Any hints?

Pecsan9mj · Accepted Answer

Let the transformation be f(x,y)=(f1(x,y),f2(x,y)).  The line y=3 is mapped to x=0 so f1(x,3)=0 for all x. This means that we can set f1(x,y)=M1(y−3) for a some constant M1. Similarly, we can set f2(x,y)=M2(x2−y).  Then we have f(x,y)=(M1(y−3),M2(x2−y)).

Constructing a transformation satisfying the given properties Construct a transformation which

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