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CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 12 - MCQExams.com
CBSE
Class 11 Engineering Maths
Conic Sections
Quiz 12
The latus rectum of parabola
y
2
=
5
x
+
4
y
+
1
is
Report Question
0%
10
0%
5
0%
5
4
0%
5
2
A circle touch the line L and the circle
C
1
externally such that both the circles are on the same side of the line, then the locus of center of the circle is
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0%
ellipse
0%
hyperbola
0%
parabola
0%
parts of straight line
The equations
x
=
t
4
,
y
=
t
2
4
represents
Report Question
0%
An ellipse
0%
A parabola
0%
A circle
0%
A hyperbola
Length of the latus rectum of the hyperbola
x
y
=
c
2
,
is
Report Question
0%
√
2
c
0%
2
c
0%
2
√
2
c
0%
4
c
Lissajous figure obtained by combining x=ASin
ω
t
and y=ASin
(
ω
t
+
Π
/
4
)
will be
Report Question
0%
an ellipse
0%
a straight line
0%
a circle
0%
a parabola
Let
P
Q
be a variable focal chord of the parabola
y
2
=
4
a
x
(
a
>
0
)
whose vertex is A. then the locus of centroid of
Δ
A
P
Q
lies on a parabola whose length of latusrectum is
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0%
2
a
3
0%
a
0%
4
a
3
0%
5
a
3
Vertex of the parabola
2
y
2
+
3
y
+
4
x
−
1
=
0
is
Report Question
0%
(
25
32
,
−
7
4
)
0%
(
25
32
,
−
3
4
)
0%
(
15
32
,
7
4
)
0%
(
17
32
,
−
3
4
)
A circle passes through
A
(
1
,
2
)
and the equations of the normal to the circle is
x
+
2
y
=
5
. If the circle passes through
B
(
−
5
,
5
)
, then the radius of the circle is
Report Question
0%
3
2
0%
√
5
2
0%
3
√
5
2
0%
5
2
If the radius of the circle
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
be
r
, then it will touch both the axes, if
Report Question
0%
g
=
f
=
c
0%
g
=
f
=
c
=
r
0%
g
=
f
=
√
c
=
r
0%
g
=
f
and
c
2
=
r
If two distinct chords of a parabola
y
2
=
4
a
x
passing through the point
(
a
,
2
a
)
are bisected by the line
x
+
y
=
1
, then the length of the latus rectum can be
Report Question
0%
(
2
,
6
)
0%
(
1
,
4
)
0%
(
0
,
2
)
0%
(
0
,
4
)
The equations
x
=
t
4
,
y
=
t
2
4
represents
Report Question
0%
An ellipse
0%
A parabola
0%
A circle
0%
A hyperbola
If the radius of the circle
x
2
+
y
2
- 18 x - 12 y + k = 0 be 11 then k =
Report Question
0%
347
0%
4
0%
-4
0%
97
The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by
Report Question
0%
24/5
0%
12/5
0%
6/5
0%
23/5
If
(
3
x
−
4
y
−
1
)
2
100
−
(
4
x
+
3
y
−
1
)
2
225
=
1
,
then
length latusrectum of hyperbola is-
Report Question
0%
9
2
0%
40
3
0%
9
0%
8
3
If
y
2
−
2
x
−
2
y
+
5
=
0
is
Report Question
0%
a circle with centre
(
1
,
1
)
0%
a parabola with vertex
0%
a parabola with directrix
x
=
3
/
2
0%
a parabola with directrix
The value of
α
for which three distinct chords drawn from
(
α
,
0
)
to the ellipse
x
2
+
2
y
2
=
1
are bisected by the parabola
y
2
=
4
x
is
Report Question
0%
9
0%
√
17
0%
8
0%
None of these.
The equation
x
2
10
−
a
+
y
2
4
−
a
=
1
, represents an ellipse , if
Report Question
0%
a
<
4
0%
a
>
4
0%
4
<
a
<
10
0%
a
>
10
Let PQ be the latus rectum of the parabola
y
2
=
4
x
with vertex A.
Minimum length of the projection of PQ on a tangent drawn in portion of parabola PAQ is :
Report Question
0%
2
0%
4
0%
2
√
3
0%
2
√
2
C
:
x
2
16
+
y
2
12
=
1
The equation of parabolas with same latus- rectum as conic C, is/are
Report Question
0%
y
2
−
5
x
+
3
=
0
0%
y
2
+
6
x
−
21
=
0
0%
y
2
−
6
x
−
21
=
0
0%
y
2
+
6
x
+
3
=
0
The distance between the foci or a hyperbola is double the distance between its vertices and the length of a conjugate axis isThe equation of the hyperbola referred to its axes as axes of coordinates is
Report Question
0%
3
x
2
−
y
2
=
3
0%
x
2
−
3
y
2
=
3
0%
3
x
2
−
y
2
=
9
0%
x
2
−
3
y
2
=
9
The equation of directrix of a parabola is 3x + 4y + 15 =0 and equation of tangent at vertex is 3x + 4y - 5=Then the length of latus recturn is equal to
Report Question
0%
15
0%
14
0%
13
0%
16
Length of the latus rectum of the parabola
25
[
(
x
−
2
)
2
+
(
y
−
3
)
2
]
=
(
3
x
−
4
y
+
7
)
2
is
Report Question
0%
4
0%
2
0%
1/5
0%
2/5
equation of latus rectum of the parabola
y
2
−
16
x
−
6
y
+
1
=
0
is
Report Question
0%
x-7=0
0%
x+7=0
0%
2x-7=0
0%
2x+7=0
The latus rectum of a parabola whose directrix is x + y- 2 =0 and focus is (3, -4) is
Report Question
0%
−
3
√
2
0%
3
√
2
0%
2
√
2
0%
3
√
2
The y-axis is the directrix of the ellipse with eccentricity e=1/2 and the corresponding focus is at (3, 0), equation to its auxilary circle is
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0%
x
2
+
y
2
−
8
x
+
12
=
0
0%
x
2
+
y
2
−
8
x
−
12
=
0
0%
x
2
+
y
2
−
8
x
+
9
=
0
0%
x
2
+
y
2
=
4
If e,e' be the eccentricities of two conics S and S' and if
e
2
+
e
,
2
=
3
, then bothe S and S'
Report Question
0%
Ellipses
0%
Parabola
0%
Hyperbola
0%
None of these
The equation of circle with centre (1, 2) and tangent
x
+
y
−
5
=
0
is
Report Question
0%
x
2
+
y
2
+
2
x
−
4
y
+
6
=
0
0%
x
2
+
y
2
−
2
x
−
4
y
+
3
=
0
0%
x
2
+
y
2
−
2
x
+
4
y
+
8
=
0
0%
x
2
+
y
2
−
2
x
−
4
y
+
8
=
0
The equation of the ellipse with axes along the x-axis and the y-axis, which passes through the points P(4, 3) and Q (6, 2) is
Report Question
0%
x
2
50
+
y
2
13
=
1
0%
x
2
52
+
y
2
13
=
1
0%
x
2
13
+
y
2
52
=
1
0%
x
2
52
+
y
2
17
=
1
If the circle describe on the line joining the points (0, 1) and
(
α
,
β
)
as diameter cuts the x-axis in points whose abscissae are roots of equation
x
2
−
x
+
3
=
0
the
(
α
,
β
)
Report Question
0%
(1, 3)
0%
(1, 5)
0%
(-5, 1)
0%
(-5, -1)
The equation of a circle with origin as a centre and passing through equilateral whose median is of length 3a is
Report Question
0%
x
2
+
y
2
=
9
a
2
0%
x
2
+
y
2
=
16
a
2
0%
x
2
+
y
2
=
a
2
0%
None of these
If the parabola
y
2
=
4
a
x
passes through (2,6) then the equation of the latusrectum is
Report Question
0%
2x -9 = 0
0%
4x + 9 = 0
0%
2x + 9 = 0
0%
4x - 9 = 0
The length of the latus rectum of the parabola
4
y
2
+
2
x
−
20
y
+
17
=
0
is
Report Question
0%
3
0%
6
0%
1
/
2
0%
None
The length of the latus rectum of the parabola
y
2
−
4
x
+
4
y
+
8
=
0
i
s
Report Question
0%
8
0%
6
0%
4
0%
2
The equation
x
2
12
−
a
+
y
2
4
−
a
=
1
represent an ellipse, if:
Report Question
0%
a
<
12
0%
a
<
4
0%
a
>
12
0%
a
>
4
The equation of circles passing through (3,-6) touching both the axes is
Report Question
0%
x
2
+
y
2
−
6
x
+
6
y
+
9
=
0
0%
x
2
+
y
2
+
6
x
−
6
y
+
9
=
0
0%
x
2
+
y
2
−
30
x
−
30
y
+
225
=
0
0%
x
2
+
y
2
−
30
x
+
30
y
+
225
=
0
If
a
≠
b
the parametric equations
x
=
a
(
c
o
s
Θ
+
s
i
n
Θ
)
,
y
=
b
(
c
o
s
Θ
−
s
i
n
Θ
)
represents
Report Question
0%
Hyperbola
0%
A circle
0%
An ellipse
0%
A pair of straight lines
0%
A parabola
A common tangent to the conics
x
2
=
6
y
and
2
x
2
−
4
y
2
=
9
, is __________.
Report Question
0%
x
+
y
=
1
0%
x
−
y
=
1
0%
x
+
y
=
9
2
0%
x
−
y
=
3
2
The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by
Report Question
0%
24/5
0%
12/5
0%
6/5
0%
none of these
The eccentricity of the hyperbola
x
2
−
3
y
2
+
1
=
0
is
Report Question
0%
1
2
0%
1
0%
2
0%
3
If
5
x
+
9
=
0
is the directrix of the hyperbola
16
x
2
−
9
y
2
=
144
, then its correponding focus is:
Report Question
0%
(
−
5
3
,
0
)
0%
(
5
,
0
)
0%
(
−
5
,
0
)
0%
(
5
3
,
0
)
Explanation
Step 1 : Convert the given equation of hyperbola in parametric form
G
i
v
e
n
:
16
x
2
−
9
y
2
=
144
⟹
16
x
2
144
−
9
y
2
144
=
1
⟹
x
2
9
−
y
2
16
=
1
.
.
.
(
i
)
⟹
a
2
=
9
⟹
a
=
3
,
b
2
=
16
.
.
.
(
i
i
)
Step 2 : Write equation of directrix in standard form
Equation of directrix to the hyperbola
x
2
a
2
−
y
2
b
2
=
1
is
x
±
a
e
=
0
Given equation of a directrix is
5
x
+
9
=
0
dividing by 5 on both sides,
⟹
x
+
9
5
=
0
∵
\implies x+\cfrac {3} {\cfrac 5 3}=0
\therefore e=\cfrac 5 3 \,\text{ and directrix lies in left side of hyperbola.}
\text{Hence corresponding focus will be at negative }X-axis.
\therefore \textbf{focus is at } \boldsymbol{(-ae,0)}\equiv (-3)\times \cfrac 53\equiv (-5, 0)
\therefore \textbf{The focus corresponding to the directrix }\,\boldsymbol{5x+9=0\,\textbf{is at }\,(-5, 0) .}
\textbf{Hence, option C is correct .}
If the centroid of an equilateral triangle is (1,1) and one of its vertices is (-1,2) then, equation of its circum circle is
Report Question
0%
x^{2}+y^{2}-2x-2y-3=0
0%
x^{2}+y^{2}+2x-2y-3=0
0%
x^{2}+y^{2}-4x-6y+9=0
0%
x^{2}+y^{2}+x-y+5=0
The eccentricity of an ellipse, with its centre at the origin, is
\frac{1}{2}
. If one of the directrices is x = 4, then the equation of the ellipse is
Report Question
0%
3x^2 + 4y^2
= 1
0%
3x^2 + 4y^2
= 12
0%
4x^2 + 3y^2
= 12
0%
4x^2 + 3y^2
= 1
Angle between the parabola
y^{2} = 4b(x - 2a + b)
and
x^{2} + 4a(y - 2b - a) = 0
at the common end of their latus rectum, is
Report Question
0%
\tan^{-1}(1)
0%
\cot^{-1}1 + \cot^{-1}\dfrac {1}{2} + \cot^{-1} \dfrac {1}{3}
0%
\tan^{-1} (\sqrt {3})
0%
\tan^{-1} (2) +\tan^{-1} (3)
Equation of a circle whose centre is in
I
quadrant as
\left(\alpha,\ \beta\right)
and touches
x-
axis will be:
Report Question
0%
x^{2}+y^{2}-2\alpha x - 2\beta y + \alpha ^{2}
0%
x^{2}+y^{2}+2\alpha x - 2\beta y + \alpha ^{2}
0%
x^{2}+y^{2}-2\alpha x + 2\beta y + \alpha ^{2}
0%
x^{2}+y^{2} + 2\alpha x + 2\beta y + \alpha ^{2}
Explanation
Given that: A circle centre in I quadrant as
(\alpha,\beta)
and touches x-axis.
To find: Equation of the circle.
Solution:
Refer image,
\therefore
Centre (c)
=(\alpha,\beta)
\because\,CP
is parallel to y-axis
\therefore
Radius (p)
=CP=\sqrt{(x_2-x_2)^2+(y_2-y_1)^2}
=\sqrt{(\alpha-\alpha)^2+(0-\beta)^2}
=\sqrt{\beta^2}
=\beta
\therefore
Equation of the circle is
(x-\alpha)^2+(y-\beta)^2=\beta^2
\Rightarrow x^2-2\alpha x+\alpha^2+y^2-2\beta y+\beta^2=\beta^2
\Rightarrow x^2+y^2-2\alpha x-2\beta y+\alpha^2=0
Hence, the required is
x^2+y^2-2\alpha x-2\beta y+\alpha^2=0
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