Find the distance of the centre of the circle x2 + y2 + z2 + x - 2y + 2z = 3, 2x + y +2z = 1 from the plane ax + by + cz = d , where a, b,c,d, are constants.
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Trace the surface x2/ 4 + y2 /9 - z2/ 4 . Also describe its sections by the planes x = ±2 , algebraically and geometrically.
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
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.
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.
Find the distance of the centre of the circle x2 + y2 + z2 + x - 2y + 2z = 3, 2x + y +2z = 1 from the plane ax + by + cz = d , where a, b,c,d, are constants.
Reduce the conic you obtained in (i) above to standard form