Analytic Geometry Answers

Center of the circle (0,0) is tangent to the line x-3y =6

Find the equation of a locus of a point so that the square of its distance from (3,-3) is always numerically equal to the slope of the line joining it to the same point

Obtain the equation of the sphere having center on the line x/3= y/2= z/-5 and passing through the points
�(0,-2,-4) and (2,-1,-1)

Find the coordinates of the foot of the perpendicular from (-2,6) on the line
2x+3y-1=0. �

Obtain the equation of the line passing through (1,-1,2) having direction ratios (2,0,1)

A ̅=5i+7j+8k

B ̅= 5i+2j-5k


Use your understanding of vector analysis to complete the following:

Calculate a resultant vector which would theoretically represent a single force that could replace the two force vectors A and B while giving the same support to the structure.

Calculate the modulus of all three forces.
Determine the value of the dot-product (scalar product) of vectors A and B
Calculate the angle between the vectors A and B
Determine the directional cosine angles of the resultant vector with respect to the x, y and z axes.

Find the equation of circle with center at the origin and tangent to the line 2x - 5y =8.

Find the standard form of the equation of circle whose center is at (4,3) which passes through the origin. Draw the circle

Identify an axis of revolution and generating conic of the surface 4x^2+25y^2+4z^2=100 . Does this conic also generates( x^2/4) +(y^2/25) + (z^2/4)=1 ? Give reason for your answer?

A rotating liquid forms a surface in the form of a paraboloid . The surface is 2m deep at the centre and 10 m across.Obtain an equation of the surface?