Omi67

What is the measure of angle θ ?

What is the value of a?

What is the length of BC¯¯¯¯¯BC¯ ?

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

There are two ways to solve it.

r²=9

The radius is 3. 

N is the point ( 4t, 2t2) on the parabola 𝑥2 = 8𝑦 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, the
midpoint of NB.


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


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

3:   A circle with center O has radius 8 units and circle P has radius 2 units. The circles are externally tangent to each other at point Q. Segment TS is the common external tangent to circle O and circle P at points T and S, respectively. What is the length of segment OS? Express your answer in simplest radical form.

1:   A right square pyramid with base edges of length 8sqrt2 units each and slant edges of length 10 units each is cut by a plane that is parallel to its base and 3 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?