Download OU B.Sc 2018 Dec 3rd Year 3186 Solid Geometry Question Paper

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Code No. 1188/E

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FACULTY OF SCIENCE

Subject - Mathematics

Paper - VIA : Solid Geometry (OSE - 1)

Time - 3 Hours Max. Marks: 50

PART - A (5 x 3 = 15 Marks)

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Answer any FIVE of the following questions:

1. Find the equation of the cone which touches the coordinate axes.
2. Find the condition that the cone ax² + by² + cz² + 2fyz + 2gzx + 2hxy = 0 with three mutually perpendicular generators.
3. Find the equation of the enveloping cone of the sphere x² + y² + z² + 2x - 2y = 2 with its vertex at (1,1,1).
4. Find the equation of the tangent planes to x² + 2y² + 3z² = 17 which pass through the line x + 2y + z = 3, x + y + z = 2.

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5. Find the equation of the sphere which touches the sphere x² + y² + z² + 2x - 4y = 0 at the point (1,2,-2) and passes through the origin.
6. Show that the plane lx + my + nz = 0 cuts the cone ayz + bzx + cxy = 0 in perpendicular lines if a + b + c = 0.
7. Find the condition that the plane lx + my + nz = p touches the conicoid ax² + by² + cz² = 1.
8. Find the locus of the vertices of the cone which touches the coordinate planes.

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