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*N *is the point ( 4*t*, 2*t ^{2}*) on the parabola đť‘Ą

(i) If this normal meets the axis of the parabola at *B*, find the locus of *E*, theâ€¨midpoint of *NB*.â€¨

(ii) The perpendicular from *D *to the normal meets it at *H*. Find the equation of *DH *and hence find the coordinates of *H*.â€¨

(iii) What relation exists between the locus of *E *and the locus of H?

Thank you :)

Yousif.m May 15, 2018

#1**+1 **

N is the point ( 4t, 2t2) on the parabola đť‘Ą2 = 8đť‘¦ whose focus is D. Find the equation of the normal at N.

(i) If this normal meets the axis of the parabola at B, find the locus of E, theâ€¨midpoint of NB.â€¨

(ii) The perpendicular from D to the normal meets it at H. Find the equation of DH and hence find the coordinates of H.â€¨

(iii) What relation exists between the locus of E and the locus of H?

Omi67 May 16, 2018