chapter 6: Conic Section
MCQ's with answers from chapter 6 Conic Section Mathematics book 2 for FSC pre engineering for Board of Intermediate and Secondary education. Also For Entry Test Preparation for UET, NUST, PIEAS, GIKI, AIR, FAST, WAH University, other engineering Universities.
8. Pair of Lines & Circles
1) The
intersection of a cone with a plane gives
A)
Point
B)
Line
C)
Conic Section
D)
Two points
Answer: C
2) The
conic sections are described today by
A)
Linear Equation
B)
Bi-Quadratic equations
C)
Quadratic equations
D)
Cubic equations
Answer: C
3) The
standard conic section are
A)
Circle
B)
Parabola
C)
Ellipse / hyperbola
D)
All A, B, C are true
Answer: D
4) The
degenerate conic sections are
A)
a point
B)
two coincident lines
C)
a pair of lines
D)
All A, B, C are true
Answer: D
5) The
equation 3x2 – 4xy + 5y2
= 0 is called
A)
Quadratic
B)
Linear
C)
Explicit
D)
Homogeneous
Answer: D
6) The
two lines represented by the equation
8x2
+ 41xy - 8y2 = 0are
A)
Parallel
B)
Non Parallel
C)
Perpendicular
D)
Coincident
Answer: C
7) If
the two lines represented by the equation
ax2
+ 2hxy + by2 = 0 are perpendicular then,
A)
a = b
B)
h = ab
C)
a + b = 0
D)
h = a + b
Answer: C
8) The
angle between the pair of lines represented by , 3x2 – 4xy – 3y2
= 0 is
A)
p/2
B)
p/3
C)
p/4
D)
p/6
Answer: A
9) The
pair of lines represented by y2 – 36 = 0 are
A)
Parallel
B)
Perpendicular
C)
Non parallel
D)
Coincident
Answer: A
10) The
center of the circle represented by the equation (x – 1)2 + (y – 2)2
= 4 is
A)
(0, 0)
B)
(1, 1)
C)
(1, 2)
D)
(1, - 2)
Answer: C
11) The
radius of the circle, represented by the equation x2 + 2x + 1 + y2 + 4y +
4 = 16 is
A)
16
B)
8
C)
11
D)
4
Answer: D
12) The
length of the diameter of the circle represented by the equation 2x2
+ 2y2 – 8 = 0, is
A)
8
B)
4
C)
2
D)
16
Answer: B
13) The
length of the chord of the circle defined by
x2 + 4x + 4 + y2
+ 6y + 9 = 9, passing through the center
is
A)
9
B)
3
C)
6
D)
4
Answer: C
14) The
circumference of the circle represented by
x2
+ 2x + 1 + y2 + 2y + 1 = 25 is
A)
2p
B)
25p
C)
10p
D)
5p
Answer: C
15) The
length of the chord of the circle
x2 – 2x + 1 + y2
– 6y + 9 = 9 passing through the point (1, 3) is
A)
9
B)
6
C)
3
D)
18
Answer: B
16) If
length of a chord of the circle x2 – 2x + 1 + y2 + 2y + 1
= 25 is 10, then it will pass through the point
A)
(-1, 1)
B)
(1, -1)
C)
(1, 5)
D)
(5, 1)
Answer: B
20) If
a point P is outside the circle then from this point we can draw
A)
one tangent to the circle
B)
two tangents to the circle
C)
three tangents to the circle
D)
no tangent to the circle
Answer: B
23) If
g2 + f2 – c = 0 then the circle reduces to
A)
a line
B)
a point
C)
two points
D)
none of these
Answer: B
24) In
the equation of a circle the coefficient of x2 and y2 are
A)
Positive
B)
Negative
C)
Equal
D)
Unequal
Answer: C
25) The
equation of a circle is an equation of
A)
Second degree in x
B)
Second degree in y
C)
First degree in x and y
D)
Second degree in x and y
Answer: D
26) In
the equation of a circle there is no term involving
A)
x
B)
y
C)
xy
D)
x2
Answer: C
27) The
equation 3x2 + 3y2
– 213x + 97y + 329 = 0 represents a
A)
Line
B)
Circle
C)
Ellipse
D)
Parabola
Answer: B
29) The
equation of the tangent to the circle x2 + y2 = 8 at the
point (2, 2) is
A)
2x + y = 8
B)
x – y = 4
C)
x + y = 2
D)
2x + y = 4
Answer: A
30) If
x2 + y2 = 4 represents a circle then the point (-2, 0)
lies
A)
Inside the circle
B)
Outside the circle
C)
On the circle
D)
None of these
Answer: C
31) If
a body is moving with a uniform angular speed around a circular path then the
linear velocity of the body is directed along
A)
The circular path
B)
The normal to the path
C)
The tangent to the path
D)
None of these
Answer: C
9. Conic Section II, Parabola, Ellipse and
Hyperbola
1) If
the conic is a parabola then the value of eccentricity is
A)
0
B)
1
C)
less than 1
D)
greater than 1
Answer: B
2) If
e = 1 then the conic is a
A)
Circle
B)
Parabola
C)
Ellipse
D)
Hyperbola
Answer: B
3) If
e < 1 then the conic is
A)
a circle
B)
a parabola
C)
an ellipse
D)
a hyperbola
Answer: C
4) If
e > 1 then the conic is
A)
a circle
B)
a parabola
C)
an ellipse
D)
a hyperbola
Answer: D
5) Locus
of points in a plane, the distance of each of which from a fixed point is equal
to its distance from a fixed straight line in the plane is called
A)
a circle
B)
a parabola
C)
an ellipse
D)
a hyperbola
Answer: B
6) Locus
of points in a plane, the distance of each of which from a fixed point is less
than its distance from a fixed line in the plane is called
A)
a circle
B)
a parabola
C)
an ellipse
D)
a hyperbola
Answer: C
7) Locus
of points in a plane, the distance of each of which from a fixed point is
greater than its distance from a fixed line in the plane is called
A)
a circle
B)
a parabola
C)
an ellipse
D)
a hyperbola
Answer: D
8) the
vertex of the parabola y2 = - 8x
is
A)
(-2, 0)
B)
(2, 0)
C)
(0, 0)
D)
(0, -2)
Answer: C
9) The
axis of the parabola x2 = - 4y is
A)
x-axis
B)
y-axis
C)
x and y-axis
D)
none of these
Answer: B
10) The
equation of the axis of the parabola y2 = 16x is
A)
x – y = 0
B)
x + y = 0
C)
x = 0
D)
y = 0
Answer: D
11) The
equation of the latus rectum of the parabola
y2
= -16x is
A)
x = 4
B)
y = -4
C)
y – 4 = 0
D)
x + 4 = 0
Answer: D
17) The
coordinates of the focus of the parabola
(x – 3)2
= 4(y – 2) is
A)
(0, 3)
B)
(0, 2)
C)
(3, 3)
D)
(3, 2)
Answer: C
18) The
coordinates of the vertex of the parabola
(x – 5)2
= 4(y – 4) is
A)
(0, 5)
B)
(0, 4)
C)
(4, 5)
D)
(5, 4)
Answer: D
19) The
equation of the axis of the parabola
(x – 3)2
= 2(y + 4) is
A)
x = -3
B)
x – 3 = 0
C)
y + 4 = 0
D)
y = 4
Answer: B
20) The equation of the Directrix of the
parabola
(x – 3)2
= 4(y – 2) is
A)
x = 1
B)
y = 2
C)
y – 1= 0
D)
y = -1
Answer: C
21) The
equation of the latus rectum of the parabola
(x +1)2
= 4(y – 2) is
A)
y – 3 = 0
B)
y = -3
C)
x = 3
D)
x = -3
Answer: A
22) the
equation of the tangent at the vertex of the parabola (x + 3)2 = 4(y
– 2) is
A)
x = -3
B)
y = 0
C)
y – 2 = 0
D)
y = -2
Answer: C
23) The
coordinates of the vertex of the parabola
(y – 3)2
= 4(x – 1) is
A)
(0, 0)
B)
(3, 1)
C)
(1, 3)
D)
(-3, -1)
Answer: C
24) The
equation of the circle whose diameter is the latus rectum of the parabola x2
= 4y is
A)
(x – 2)2 + (y – 1)2 = 4
B)
x 2 + (y – 1)2 = 2
C)
x 2 + (y + 1)2 = 4
D)
x 2 + (y – 1)2 = 4
Answer: D
27) In
an ellipse the mid point C of the major axis is called
A)
The center of the ellipse
B)
Focus of the ellipse
C)
Vertex of the ellipse
D)
Second focus
Answer: A
28) The
curve of the parabola y2 = 4ax is symmetrical with respect to
A)
Origin
B)
X-axis
C)
Y-axis
D)
Both the axis
Answer: B
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