Download OU B.Sc 2019 Dec 5th Sem (3rd Year) 8188E Mathematics (Solid Geometry) Question Paper

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Code No: 8188

B.Sc. V-Semester (CBCS) Examination, November | December 2019

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Subject : Mathematics (Solid Geometry)

Paper - VIA

Max. Marks: 60

PART - A (5 X 3 = 15 Marks)

(Short Answer Type)

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Note : Answer any FIVE of the following questions.

1. Find the equation of the sphere which passes through the points (0,0,0), A(1, 2, 3), B(1, -2, 3), C(1, 2, -3)
2. Find the points of intersection of the line 2x - 1 = y+3 = -2z +4 with the sphere x² + y² + z² -6x+8y-4z+4=0
3. Find the equation of the cone with vertex at 0(0, 0, 0) and passing through the circle x²+y²+z²+x-2y+3z-4=0, x-y+z=2
4. Find the equation of the cylinder with generators parallel to x — axis and passing through a²x² +b²y²=2cz, lx+my+nz=p

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5. Find the equation of the tangent plane to the conicoid 3x² - 5y² + 2z² +2 = 0 at point P(1,1,0).
6. Find the points of intersection of the line x/3 = y/-2 = z/1 with the conicoid 23x² - 17y² + 7z² =7
7. Find the condition that the spheres x² + y² + z² + 2lx + 2my +p=0 and x² + y² + z² = k² may cut orthogonally
8. Find the equation of the reciprocal to the cone 5x² + 9y² + 11z² = 0

PART - B (3 x 15 = 45 Marks)

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(Essay Answer Type)

Note: Answer ALL questions.

1. If a tangent plane to the sphere x² + y² + z² = a² makes intercepts a, b, and c on the coordinate axes, prove that 1/a² + 1/b² + 1/c² = 1/a²
   OR
2. Find the equation of the cone whose vertex is A(1, 2, 3) and guiding curve is the circle x² + y² + z² = 4, x+y+z=1
   

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   OR
3. Find the equation of the cylinder whose generators are parallel to x/1 = y/-2 = z/3 and whose guiding curve is the ellipse x² + 2y² = 1, z=0.
4. If the section of the paraboloid x² + 4y² = 6z by the plane lx + my + nz = p meets the coordinate axes in P, Q, R, find the coordinates of the centroid of triangle PQR.

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