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D 30563 (Pages : 3) 1۹٦8123 61777757, ಆ 555೮ ‏ممم ململ‎

FIFTH SEMESTER (CBCSS-UG) DEGREE EXAMINATION
NOVEMBER 2022

Mathematics
MTS 5B 09—INTRODUCTION TO GEOMETRY
(2019 Admission only)
Time : Two Hours Maximum : 60 Marks
Section A

Answer any number of questions.
Each question carries 2 marks.
Ceiling is 20.

1. Find focus, vertex and directrix of the parabola y? = 2x.

2. Determine the equation of the tangent at the point P with parameter ¢ on the rectangular hyperbola

; 1
with parametric equations x =f, y= 5

3. Find the equation of the normal to the parabola with parametric equations x = 2¢2, y = 4¢ at the
point with parameter ¢ = 3.

4, Write the equation of the conic 11x? + 4xy + 14y” — 4x — 28y —16 = 0 in matrix form.
5. Prove that if ¢, is an Eucledean transformation of R? given by t; (X)=UX+a,Xe R?, then:

i) The transformation of R? given by tf) (X)=U'X -U ‘a, Xe R? is also a Euclidean
transformation.
ii) The transformation ‏و2‎ is the inverse of t,.
6. Prove that Euclidean congruence is an equivalence relation.

7. Determine the affine transformation which maps the points (0, 0), (1, 0) and (0, 1) to the points
(3, 2), (5, 8) and (7, 3) respectively.

8. Prove that an affine transformation maps parallel straight lines to parallel straight lines.

Turn over

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