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Published on: 29/08/2019
Conic Sections
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Questions + Answers key
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1.
The latus rectum of the hyperbola \({ 16x }^{ 2 }-{ ay }^{ 2 }=144\quad is\) _______.
323
\(\frac { 15 }{ 4 } \)
\(\frac { 4 }{ 3 } \)
\(\frac { 3 }{ 4 } \)
2.
The difference of the focal distances of any point on the hyperbola is equal to ______.
length of conjugate axis
length of transverse axis
latus rectum
none of these
3.
The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is _______.
\(\frac { 1 }{ 2 } \)
\(\sqrt { \frac { 1 }{ 3 } } \)
\(\sqrt { \frac { 2 }{ 3 } } \)
\(\sqrt { \frac { 3 }{ 2 } } \)
4.
The difference between the lengths of the major axis and the latus rectum of an ellipse is ______.
\({ 2ae }^{ 2 }\)
\(ae\)
\(3ae\)
\(ae^{ 2 }\)
5.
The eccentricity of the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) if its latus rectum is equal to one half of its minor axis is _______.
\(\frac { 1 }{ 2 } \)
\(\frac { \sqrt { 3 } }{ 2 } \)
\(\frac { 1 }{ \sqrt { 3 } } \)
None of these
6.
In the parabola y2 = 4ax,the length of the chord passing through the vertex and inclined to the axis at π/4 is ________.
\(4\sqrt { 2 } a\)
\(3\sqrt { 2 } a\)
\(2\sqrt { 2 } a\)
\(\sqrt { 2 } a\)
7.
The locus of the points of trisection of the double ordinates of a parabola is a ______.
pair of lines
parabola
circles
none of these
8.
The four distinct points (0,0), (2,0), (0,−2) and (k,−2) are concyclic if k is equal to ______.
-1
-2
2
0
9.
If the circle x2+y2+2ax+c = 0 and x2+y2+2by+c = 0 touch each other then ______.
\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ c } \)
\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ { c }^{ 2 } } \)
\(\frac { 1 }{ a } +\frac { 1 }{ b } =\frac { 1 }{ c } \)
None of these
10.
The circle x2+y2+2gx+2fy+c = 0 does not intersect x − axis if ______.
\(g^{ 2 }>c\)
\(g^{ 2 }
\(g^{ 2 }>2c\)
\(g^{ 2 }<2c\)
1.
(a)
323
2.
(b)
length of transverse axis
3.
(d)
\(\sqrt { \frac { 3 }{ 2 } } \)
4.
(a)
\({ 2ae }^{ 2 }\)
5.
(b)
\(\frac { \sqrt { 3 } }{ 2 } \)
6.
(a)
\(4\sqrt { 2 } a\)
7.
(b)
parabola
8.
(c)
2
9.
(a)
\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ c } \)
10.
(a)
\(g^{ 2 }>c\)
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