D 10670 (Pages : 3) फिल्लाव6.,....५०००००००००००००००००००००००००००००००००००

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एटीएम, ००० «पर ००५५५५००
FIFTH SEMESTER U.G. DEGREE EXAMINATION, NOVEMBER 2021
(CBCSS—UG)
Mathematics
MTS 5B 09—INTRODUCTION TO GEOMETRY
(2019 Admissions)
: Two Hours Maximum : 60 Marks
Section A

Answer at least eight questions.
Each question carries 3 marks.
All questions can be attended.

Overall Ceiling 24.

Find the equation of the tangent at the point with parameter ¢ to the parabola with parametric

equations x =at?, y =2at wheret €R.

Let E be a parabola with parametric equations x =t?, y=t,t¢R. Find focus, vertex axis and
directrix of E.
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Prove that the equation of the tangent at the point (x, y,) to an ellipse is 38 + एप = 1.
Write the equation of the conic x? — 4xy + 4y? — 6x —8y +5 =0 in matrix form.
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Show that 5170 0080 | i$ orthogonal for each real number 0.
Let the Euclidean transformations ¢, ೩೧6 of IR? be given by :
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5 5 1
t,(x)=|® 5 |x+| — | and
4 3|""|-2
5 5
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5 5 -2 Fin
ty (X)= 3 4 ன்‌ £ (षण ty ot}.
5 5 Turn over

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