Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B-Sc CSE-IT (Bachelor of Science in Computer Science) 2020 March 2nd Sem 71507 Coordinate Geometry Previous Question Paper
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (CS) (2013 & Onwards) (Sem.?2)
COORDINATE GEOMETRY
Subject Code : BCS-202
M.Code : 71507
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.
SECTION?A
1. Answer briefly :
a) Define an ellipse and a parabola.
b) Find the equation of the ellipse having major axis along x-axis and minor axis along
y-axis, eccentricity
1
,
2
and the distance between the foci as 4.
c) Find the equation to the two straight lines through the origin perpendicular to the lines
5x
2
? 7xy ? 3y
2
= 0.
d) Find the points of the parabola y
2
= 8x, whose ordinate is twice the abscissa.
e) State and prove the reciprocal property of pole and polar with respect to a parabola.
f) Find the equation to the circle which passes through the points (1, 0), (0, ?6) and
(3, 4).
g) Find the equation of normal to a parabola in the slope form.
h) Find the equation of the hyperbola whose asymptotes are the lines x + 2y + 1 = 0 and
2x + y + 3 = 0 and which passes through the point (1, 2)
i) Find the transformed equation of 17x
2
?16xy + 17y
2
?225 = 0 when the axes are rotated
through an angle of 45?.
j) Find the equations of the straight lines bisecting the angles between the pair of
straight lines 4x
2
? 16xy + 7y
2
= 0
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1 | M- 71507 (S3)-2225
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (CS) (2013 & Onwards) (Sem.?2)
COORDINATE GEOMETRY
Subject Code : BCS-202
M.Code : 71507
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt any FOUR questions.
SECTION?A
1. Answer briefly :
a) Define an ellipse and a parabola.
b) Find the equation of the ellipse having major axis along x-axis and minor axis along
y-axis, eccentricity
1
,
2
and the distance between the foci as 4.
c) Find the equation to the two straight lines through the origin perpendicular to the lines
5x
2
? 7xy ? 3y
2
= 0.
d) Find the points of the parabola y
2
= 8x, whose ordinate is twice the abscissa.
e) State and prove the reciprocal property of pole and polar with respect to a parabola.
f) Find the equation to the circle which passes through the points (1, 0), (0, ?6) and
(3, 4).
g) Find the equation of normal to a parabola in the slope form.
h) Find the equation of the hyperbola whose asymptotes are the lines x + 2y + 1 = 0 and
2x + y + 3 = 0 and which passes through the point (1, 2)
i) Find the transformed equation of 17x
2
?16xy + 17y
2
?225 = 0 when the axes are rotated
through an angle of 45?.
j) Find the equations of the straight lines bisecting the angles between the pair of
straight lines 4x
2
? 16xy + 7y
2
= 0
2 | M- 71507 (S3)-2225
SECTION-B
2. a) On shifting the origin to the point (1, ?1) the axes remaining parallel to the original
axis, the equation of a curve becomes 4x
2
+ y
2
+ 3x ? 4y + 2 = 0. Find its original
equation.
b) Find the value of ? for which the equation 12x
2
? 10xy + 2y
2
+ 11x ? 5y + ? = 0
represents a pair of straight lines. Also find the angle between them.
3. a) Find the equation of tangent to the circle x
2
+ y
2
= a
2
which is parallel to the straight
line y = mx + c.
b) Define polar of a point. Find the polar of the point (1, 2) with respect to the circle
x
2
+ y
2
= 7.
4. a) Define orthogonal circles. Prove that the pair of circles x
2
+ y
2
? 2ax + c = 0 x
2
+ y
2
+
2by ? c = 0 intersect orthogonally.
b) Show that the lines joining the origin to the points of intersection of
x
2
+ y
2
+ 2gx + c = 0 and x
2
+ y
2
+ 2fy ? c = 0 are at right angles if g
2
? f
2
= 2c.
5. a) Find the equation of chord of the parabola y
2
= 4ax in terms of its middle point
(x
1
, y
1
).
b) Define a parabola. If chords of the parabola y
2
= 4ax are drawn at fixed distance ?a?
from the focus, show that the locus of their poles w.r.t. the parabola is
y
2
= 4x (2a + x).
6. a) Show that the line x + 2y ? 4 = 0 touches the ellipse 3x
2
+ 4y
2
= 12. Also find the
point of contact.
b) Prove that the locus of the middle points of normal chords of the rectangular
hyperbola x
2
? y
2
=a
2
is (y
2
? x
2
)
3
= 4a
2
x
2
y
2
.
7. a) Define a conjugate hyperbola. Prove that if a pair of diameters be conjugate w.r.t. a
hyperbola then they will also be conjugate w.r.t. the conjugate hyperbola.
b) Find the eccentricity, the foci and directrices of the elipse
3x
2
+ 4y
2
? 12x ? 8y + 4 = 0.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 01 April 2020