Sketch the parabola x^{2} = 4** b**y . The tangent and normal at a point P( 2bt, bt

meet the axis

of the parabola in D, E respectively.

(i) Find the coordinates of D and E.

(ii) Show that the focus Q is the midpoint of DE.

(iii) Hence prove that Q is the centre of a circle through D, P, E.

(iv) If the normal at P intersects the x-axis in F find F and the length of PF. Hence prove that PF:PD = t:2

Yousif.m May 17, 2018

#1**+2 **

Sketch the parabola x2 = 4by . The tangent and normal at a point P( 2bt, bt2)

meet the axis

of the parabola in D, E respectively.

(i) Find the coordinates of D and E.

(ii) Show that the focus Q is the midpoint of DE.

(iii) Hence prove that Q is the centre of a circle through D, P, E.

(iv) If the normal at P intersects the x-axis in F find F and the length of PF. Hence prove that PF:PD = t:2

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Omi67 May 17, 2018