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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

Yousif.m  May 17, 2018
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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

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