Analytic Geometry Answers

Find the line of intersection of the two planes x+3y+z=5 and 4x+y+2z=15

Find the equation of the plane through the following three points:
(1,2,3) (2,4,5) and (4,5,7)

Find the polar equation of the line L perpendicular to the line angle=pi/3 at P(4,pi/3)

the orthocentre of the triangle formed by the lines x+y+1=0,x-y-1=0,3x+4y+5=0 is

a and b are vectors defined by a = 8i + 2j - 3k and b = 3i - 6j + 4k, where I,j,k are mutually perpendicular unit vectors. Calculate a and b.

a. 1
b. 0
c. 2
d. 4

a and b are vectors defined by a = 8i + 2j - 3k and b = 3i - 6j + 4k, where I,j,k are mutually perpendicular unit vectors. Show that a and b are perpendicular to each other.

a. 90
b. 45
c. 1
d. 0

Find the direction cosines of the perpendicular from the origin to the plane r.(6I+4j+2root3)+2=0

a circle has the equation x(to the power of 2)+y(to the power of 2)+12x+8y+7=0

a) write down the coordinates of the centre C

b) i) show that the line with equation x=13-2y is a tangent to the circle.

ii) find the coordinates of the point Q where the tangent and circle meet

c) the point P lies on the given line such that PQ=QC. Find the two possible coordinates of P

PN is any chord of the parabola y2 =4ax; the point M divides PN in the ratio m:n.find the locus of M.

show that the straight line x(p+2q)+y(p+3q)=p+q passes through a fixed point for different values of p and q