Question

If the circumcentre of a triangle lies at the origin and centroid is the middle point of the line joining the points (a2 + 1, a2 + 1) and (2a, –2a), then the orthocenter lies on the line.

Solution

Correct option is

(a –1)2 x – (a + 1)2 y = 0

 

We know from geometry that the circumcentre, centroid and orthocentre of a triangle lie on a line. So the orthocentre of the triangle lies on the line joining the circumcentre (0, 0) and the centroid  

                 

  

SIMILAR QUESTIONS

Q1

Orthocenter of the triangle with vertices (0,0), (3, 4) and (4, 0) is

Q2

The number of integral points (integral point means both the coordinates should be integer) that lie exactly in the interior of the triangle with vertices (0, 0), (0, 21), and (21, 0) is

Q3

Let P = (–1, 0), Q = (0, 0) and  be three points. Then the equation of the bisector of the angle PQR is 

Q4

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then the point O divides the segment PQ in the ratio.

Q5

Let A0A1 2 A3 A4 A5 be a regular hexagon described in a circle of unit radius. Then the product of the length of the line segments A A1A0 A2and A0 A4 is 

Q6

 

The diagonals of a parallelogram PQRS are long the lines

x + 3y = 4 and 6x – 2y = 7, then PQRS must be a

Q7

The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is 

Q8

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

Q9

If sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

Q10

If abc are unequal and different from 1 such that the points  are collinear, then