Analytic Geometry Answers

The tangent to the parabola y²= 4ax at the point P(at² , 2at) meets the x-axis at A and the y-axis at B. Find the equation of the locus of the mid-point of AB at t varies.

 Show that the line x + y − 2 = 0 is a tangent to the parabola x²+ 8y = 0 and find the position vector of the point of contact.

The lines joining the origin to the points of intersection of the line lx + my = 1 and y²= 4ax are at right angles. Show that 4al = 1.

If the position vector of one end of a chord through the focus of the parabola y²= 8x is 1/2i + 2j, find the position vector of the other end.

How many angles are found in between 0 and 2π that satisfy the equation ItanxI = 5 ?

Given the conic section -3.6x²+1.6y²+72x+6.4y = 58/5

a) State the nature of the conic section

b) Find the characteristic elements of the conic section

c) Sketch the conic section indicating all the elements.

A conic (E) has equation y²+2y+8x+9=0

a) State the nature of (E)

b) Determine its characteristic elements

c) Sketch (E) indicating all the elements.

d) Find the length of the lactus.

Decompose the following into partial fractions

3)5x2+20x+6 / x3+2x2+x

4) x2+2x+3 / (x+1)(x2+2x+4)