Analytic Geometry Answers

How are the points (3, 5) and (5, 3) different?

Define the type of x^2+10x-4y^2+4y+24=0 and plot it.

(1)The scalar product of vectors a and b, where θ is the angle between them, is ......

(2)Determine the gradient of a straight line passing through the point (1, 6) and (-3, -3).

(3)Given a circle with centre at the origin, which passes through the point ( 2,-1). Find its equation.

(4)Find the unit vector in the direction of vector b = 3i + 4j -5k

(5)A line AB passes through the point P (3, -2) with gradient дљН 2. Determine the equation of the line CD through P perpendicular to AB

(6)Determine the equation of a straight line passing through the point (1, 0) and (2, -3).

(7)Determine the scalar product of vectors 2i+3j−5k2i+3j−5k and 4i+j−6k

(8)Find the equation of the line which is parallel to the line 2y + 3x = 3 and passes through the midpoint of (-2,3) and (4, 5).

(9)Find the centre and radius of each of the circle x2+y2 дљН2xдљН6y=15

(10)Determine the direction cosines [l, m, n] of the vector 3i -2 j +6k

(1) If r = 2i дљН 4j, s = 2i + 6j, t = 3i дус j, find 2r-t+s

(2)Find the equation of the tangent to the curve y=x3−x2y=x3−x2 at the point (1, 0).

(3)Find the area of a triangle with vertices (3, 1), (0, 0) and (1, 2).

(4)If the point C(2,−1) be the centre of a circle that passes through the point A(-2,2) find the equation of the cycle

(5)If r = 2i дљН 4j, s = 2i + 6j, t = 3i дус j, find magnitude of the vector 2r-t+s

(6)P, Q and R are points (1, -6), (3, 6) and (5, 2) respectively. Determine the length of the line joining the mid point of PQ and QR

(7)Find the equation of a straight line passing through the points (2, 3) and (-2, 5).

(8)Let Z1=6iдљН4j+4kZ1=6iдљН4j+4k, Z2=i+6j−kZ2=i+6j−k, find magnitude of th

(9)Find the equation of the normal to the curve y=x3−x2y=x3−x2 at the point (1, 1

Find the equation of the line which is parallel to the line 2y+3x=3 and passes through the midpoint of (-2,3) and (4,5)

if a vector X is represented as [xsinθi +ysinθj] then another vector Y which is normal to X can be represented as

Find the equation of the line which is parallel to the 2y+3x=3 and passes through the midpoint (-2,3) and (4,5)

Determine the gradient of a straight line passing through the point (1,6) and (-3,-3)

A line AB passes through the point P(3,-2) with gradient -1/2, determine the equation of the line CD through P perpendicular to AB.

A line AB passes through the point P(3,-2) with gradient -1/2, determine the equation of the line CD through P perpendicular to AB.