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Delhi University MCA Geometry Previous Year Questions (PYQs)
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Delhi University MCA Geometry Previous Year Questions (PYQs)
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Delhi University MCA
Previous Year Questions
Delhi University MCA
Previous Year Questions
Delhi University MCA
Qus : 1
2
The locus of the point (α, β) such that the line y = αx + β, become a tangent to the hyperbola 9x
2
- 4x
2
= 36, is
1
a hyperbola with eccentricity √5/2
2
a hyperbola with eccentricity √5
3
an ellipse with length of semi-major axis 3
4
an ellipse with eccentricity √3/2
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Qus : 2
4
The area (in squares units) of the quadrilateral formed by the tangent lines drawn to the ellipse
at the ends of its two latus rectums is
1
125/2
2
125/4
3
75/5
4
75
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Solution
Qus : 3
1
The equation 2x
2
+ y
2
- 12x - 4y + 16 = 0 represents
1
an ellipse with center (2,3)
2
a hyperbola with eccentricity √2
3
an ellipse with eccentricity 1/√2
4
a hyperbola with center (3,2)
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Qus : 4
4
The equation of common tangent to the curve y
2
= 8x and xy = - 1 is
1
3y = 9x + 2
2
y = 2x+1
3
2y = x + 8
4
y = x + 2
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Solution
Solution:
Let the common tangent be:
y
=
m
x
+
c
For curve
y
2
=
8
x
:
Condition for tangency gives:
m
c
=
2
(1)
For curve
x
y
=
−
1
:
Condition for tangency gives:
c
2
=
4
m
(2)
Substitute
c
=
2
m
from (1) into (2):
(
2
m
)
2
=
4
m
⇒
4
m
2
=
4
m
⇒
m
3
=
1
⇒
m
=
1
Then,
c
=
2
1
=
2
Final Answer:
y
=
x
+
2
Qus : 5
3
1
(a)
2
(b)
3
(c)
4
(d)
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Qus : 6
3
1
(a)
2
(b)
3
(c)
4
(d)
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Solution
Qus : 7
4
1
(a)
2
(b)
3
(c)
4
(d)
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Solution
Qus : 8
3
1
(a)
2
(b)
3
(c)
4
(d)
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Solution
Qus : 9
4
1
(a)
2
(b)
3
(c)
4
(d)
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Solution
Qus : 10
1
1
(a)
2
(b)
3
(c)
4
(d)
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Solution
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