Geometric Construction 14



In this drawing:
show that the point Q is located at
.

Show that if
then h(b)=g(b),h(a)=f(a). If in addition we also have f(c)=g(c), then f(c)=h(c)=g(c). (Aitken's Lemma)


Given Q1(x1,y1),Q2(x2,y2) and Q3(x3,y3),
construct the graph of the polynomial p(x) satisfying
p(x1) = y1, p(x2) = y2, p(x3) = y3.
        
        
        

Given (x1,y1), (x2,y2), (x3,y3) and (x4,y4), construct the graph of the polynomial p(x) satisfying
p(x1) = y1, p(x2) = y2, p(x3) = y3, p(x4) = y4 .
        
        

Given four points p0, p1,p2,p3,
we are to construct the Bezier cubic curve passing through these points as follows:
 
    The locus of p0123 forms the required curve.
        
Show that

Construct the parabola tangent to two given straight lines at two given points on each of the lines.