Book Maths Puzzle Co-ordinate geometry

The standard equation of an ellipse is
(x^2/a^2)+(y^2/b^2)=1

Write down the equations of the tangent and the normal to the

Read Solution (Total 0)

Book Other Question

Help would be much appreciated with the following question.
The standard equation of a parabola is
y^2=4ax

A general point on this curve has co-ordianates x=at^2, y=2at where t is a (variable) parameter. A point P on the curve has co-ordinates x=a(t1)^2,

y=2a(t1). A chord is drawn through P to meet the parabola again at Q, which has co-ordinates x=a(t2)^2, y=2a(t2). If this chord passes through the focus S =(a,0) of the parabola find a simple relationship between (t1) and (t2).
Find the point at which the tangents to the parabola at P and Q meet.
(t1) is my notation for t with a subscript 1
(t2) is my notation for t with a subscript 2. A box is to be formed from a rectangular piece of sheet metal by cutting squares measuring 5 inches on a side and then folding the sides. The piece of sheet metal is twice as long as it is wide. If the volume of the box is to be 1760 inches cubed, what are the dimensions of the original piece of sheet metal?