Mathematics BS Mathematics/MS Mathematics 2 Semester/Term PU — University of the Punjab 2012

UNIVERSIFY OF FIN PUNJAB M

Second Semester

2012

Exention: B.S. 4 Year Pr

Roll No

PAPER: Mathematics A-IT C

Course Code: MTH-12309

TIME ALLOWED: 2 hrs. & 30 mins.

MAX. MARKS: 60

Attempt this Paper on Separate Answer Sheet provided.

Q.2. SHORT QUESTIONS.

(10 × 3 = 30 marks)

1）

Pind te equation of tie nornal to te prbol y" E Aes in tc tim

y = mx - 2am - am' (6.2).

4/1 من

Identify the graph of the polar equation r =

Find the points at which r = 1 + cos 0 has horizontal and vertical tangents.

※iy）

v)

Locate the points of relative extrema of /

(e) :. x

r・バょ八8

Find the leagth of' the arc ol' ue curve x = e' sin #,y = e° cosO irom

8=0100=2・

vi)

Pincl the radius of curvature at auy. point on the curve x = a(t - sin t),

y = a (1 - cos t), a > 0

vii)

Find the equation of the plane which is perpendicular bisector of the line-

segment joining the pints. (3,4, -1) and (5, 2,7)

viii)

Find the spherical coordinates of the point whosc rectangular coordinates

are (-2, V3, 4).

- _

R: 387(1x)

Find an equation of the cone whose directrix is y? = x, z = and and whose

vertex is at A (0, 2, 0).

x）

1% is a complex number, prove that 5%

：•产（】

SUBJECTIVE QUESTIONS

(6 x. 5 = 30 marks)

Show that the pedal equation of the clipsc

62/14:3

Pg3HC

Find the area of the region bounded by the circle r = a and the curve r = a sin 20

Show that the intensic equation of the astrod 2 - y= a is S= 3 sin? a.

9o218 86. Vind the equation of the straight line pissing Itrough the point /(2, 9,-2) aut

perpendicular to each of the straight lines:

5 -24=

nd= = 4 = 22

Q.7. Find the cquation ot the sphero passing trough te points (0,-2,-A) and

(2, -1, -1) and having its centre on the, line: 2x

• Зу : 0 = Бу +2%.

_ Find the fourth roots of -2V3 - 2i