Analytic Geometry Answers

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)

Calculate the area of the triangle through the points (5,3,2),(-2,7,-1) and (4,-2,6)

Find the equation of the plane through the points (1,-2,4) ,(3,1,-2) and (2,-1,6)

A line passes through the points (7,-4,8) and (9,0,5)

i) Determine the parametric and symmetric equations of the line

ii)Find any other point on the line

iii)Show that the line does not pass through the origin

Find the area of the triangle determined by the points (2,-1,0),(2,0,4) and (0,2,3)

Find the perpendicular distance from point (1,-1,4) to the plane 2x-3y-2z=7