Origin O is the orthocnetre of ΔABC where A=(5,-1), B=(-2,3) then the orthocentre of ΔOAC isa)(-4,-7) b)(3,-2) c)(-2,3) d)(5,-1)Please explain.

\tThe locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)

show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0

A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.

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