COORDINATE GEOMETRY | EXAMPLES | LECTURE (11) | KARAN SONI

The coordinates of the mid points of sides AB, BC and CA of A B C are D(1,2,-3),\ E(3,0,1)a n d\ F(-1,1,-4) respectively. Write the coordinates of its centroid.

The coordinates of the mid points of sides AB, BC and CA of A B C are D(1,2,-3),\ E(3,0,1)a n d\ F(-1,1,-4) respectively. Write the coordinates of its centroid.

ABC is a triangle and AD is the median. If the coordinates of A are (4,7,-8) and the coordinates of centroid of triangle ABC are (1,1,1) what are the coordinates of D? (A) ((-1)/2,2,11) (B) ((-1)/2,-2,11/2) (C) (-1,2,11) (D) (-5,-11,19)

Find the new coordinates of (2,3) if (i) Origin is shifted to (1,1) (ii) Axis are rotated by an angle of 45^(@) in anticlockwise sence.

Tangent is drawn at the point (-1,1) on the hyperbola 3x^2-4y^2+1=0 . The area bounded by the tangent and the coordinates axes is

In a uniform electric field, the potential is 10V at the origin of coordinates , and 8 V at each of the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). The potential at the point (1, 1,1 ) will be .

Use a graph paper for this question. (Take 2 cm = 1 unit on both x and y axes) Reflect points B(2,3), C(1,1), D(2,0) on the y-axis and write down their coordinates. Name the images as B', C', D' respectively.

A straight line with slope 2 and y-intercept 5 touches the circle x^2+y^2+16 x+12 y+c=0 at a point Q . Then the coordinates of Q are (a) (-6,11) (b) (-9,-13) (c) (-10 ,-15) (d) (-6,-7)

A particle is displaced from A=(2,2,4) to B=(5, -3,-1) . A constant force of 34N acts in the direction of vec(AP) . Where P=(10,2,-11) . (Coordinates are in m). (i) Find the (vec(F)) . (ii) Find the work done by the force to cause a displacement.

Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y^2+16x+12y+c=0 at a point Q , then the coordinates of Q are (A) (-6,-11) (B) (-9,-13) (C) (-10,-15) (D) (-6,-7)