Analytic Geometry Answers

Find the co-ordinates of the orthocentre of the triangle, the equations of whose sides are x + y = 1,2x + 3y = 6, 4x − y + 4 = 0, without finding the co−ordinates of its vertices.

Trisect the segment connecting P(-5,2) and Q(3,-4).

Find y so that the length of the segment joining P(-2, 1) and Q(3, y) is square root of 34.

Find x so that the length of the segment joining P1(x, 3) and P2(-1, 4) is square root of 10.

A circle has its center at C(-3,-2) and radius square root of 76. Find the length of its chord bisected at M(4,-1).

Find the radius of a circle with center at C(1,1), if a chord of length 6 is bisected at M(3,4)

Verify if the given point is collinear. (COLLINEAR POINT lie on a straight line)
> (0.-4), (2,0), (3,2)

Find the equation of the pair of straight lines joining the origin to the points of intersection of the circles represented by x^2 + y^2 = a^2 and x^2 + y^2 + 2 ( gx + fy ) = 0.

Let
A=i−2j−3k
and
B=2i+3j+k
. Find
|A×B|

(√101)

(√191)

(√195)

(√121)

Evaluate
(2i−4k)×(i+2j)

8i−4j+4k

2i+4j+3k

3i+4j+2k

5i−3j−k