dentify an axis of revolution and generating conic of the surface
4x2 + 25y2 + 4z2 = 100 . Does this conic also generate x2/4 + y2/25 + z2/4 = 1? Give reasons for your answer.
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A rotating liquid forms a surface in the form of a paraboloid. The surface is 2m deep at the centre and 10m across. Obtain an equation of the surface.
If x/1 = y /1 = z/-1 represents one of the three mutually perpendicular generators of the cone 3xy + 8xz - 5yz = 0 , find the equations of the other two.
Find the equations of those tangent planes to the sphere x2 + y2 + z2 + 2x - 6z - 7 = 0 which intersect in the line 6x - 3y - 23 = 0, 3z + 2 = 0
Find the locus of the point, the absolute value of the difference of the distances of which from the points (2,2) and (0,0) , is 2 . Identify the curve represented by the locus.
Check whether or not the conicoid represented by 5x2 + 4y2 - 4yz + 2xz + 2x - 4y - 8z + 2 = 0 is central or not. If it is, transform the equation by shifting the origin to the centre. Else, change any one coefficient to make the equation that of a central conicoid.
Find the equation of the conic of which one focus lies at (2, 1), one directrix x + y = 0 and it passes through (4,1) . Also identify the conic.