LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

**B.Sc.** DEGREE EXAMINATION – **MATHEMATICS**

FIRST SEMESTER – NOVEMBER 2012

# MT 1500 – ALGEBRA, ANALY. GEO., CALCULUS & TRIGONOMETRY

Date : 08/11/2012 Dept. No. Max. : 100 Marks

Time : 1:00 – 4:00

__PART – A__

** **

**Answer ALL the questions: (10 x 2 = 20 marks)**

** **

- Write the n
^{th}derivative of - If y = a show that
- Define the evolute of a curve.
- Find the p-r equation of the curve r = a sin q.
- Determine the quadratic equation having 3 – 2 i as a root.
- Diminish the roots of by 2.
- Show that
- Express in locus of logarithmic function.
- Define a rectangular hyporbola.
- Write down the angle between the asymptotes of the hyperbola

__PART – B__

**Answer any FIVE questions: (5 x 8 = 40 marks)**

** **

- Show that in the parabola the subtangent at any point is double the abscissa and the subnormal is a constant.
- Find the radius of curvature at the point ‘O’ on
- Show that if the roots of
- Find the p-r equation of the curve with respect to the focus as the pole.
- Separate into real and uniaguinary parts.
- Find the sum of the series
- Find the locus of poles of ale Laugets to with respect to
- Derive the polar equation of a comic.

__ __

__PART – C__

**Answer any TWO questions: ( 2 x 20 = 40 marks)**

** **

- a) If prove that
- b) Show that r = a sec
^{2}and r = b cosec^{2}intersect at right angles. - a) Find the minimum value of
- b) Find the radius of curvature of .
- a) Solve: given that the roots are in geometric progression.

- b) Solve: .

- a) Express cos8q in locus of power of sinq.

- b) If e
_{1}and e_{2}are the eccentricities of a hyperbola and its conjugate show that .

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