The circle x²+y²+2gx+2fy+c = 0 does not intersect x − axis if ______.

1

(a)

\(g^{ 2 }>c\)

(b)

\(g^{ 2 }

(c)

\(g^{ 2 }>2c\)

(d)

\(g^{ 2 }<2c\)

 

If the circle x²+y²+2ax+c = 0 and x²+y²+2by+c = 0 touch each other then ______.

1

(a)

\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ c } \)

(b)

\(\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } =\frac { 1 }{ { c }^{ 2 } } \)

(c)

\(\frac { 1 }{ a } +\frac { 1 }{ b } =\frac { 1 }{ c } \)

(d)

None of these

 

The four distinct points (0,0), (2,0), (0,−2) and (k,−2) are concyclic if k is equal to ______.

1

(a)

-1

(b)

-2

(c)

2

(d)

0

The locus of the points of trisection of the double ordinates of a parabola is a ______.

1

(a)

pair of lines

(b)

parabola

(c)

circles

(d)

none of these

In the parabola y2 = 4ax,the length of the chord passing through the vertex and inclined to the axis at π/4 is ________.

1

(a)

\(4\sqrt { 2 } a\)

(b)

\(3\sqrt { 2 } a\)

(c)

\(2\sqrt { 2 } a\)

(d)

\(\sqrt { 2 } a\)

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 _______.

1

(a)

\(\frac { 1 }{ 2 } \)

(b)

\(\frac { \sqrt { 3 } }{ 2 } \)

(c)

\(\frac { 1 }{ \sqrt { 3 } } \)

(d)

None of these

The difference between the lengths of the major axis and the latus rectum of an ellipse is ______.

1

(a)

\({ 2ae }^{ 2 }\)

(b)

\(ae\)

(c)

\(3ae\)

(d)

\(ae^{ 2 }\)

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is _______.

1

(a)

\(\frac { 1 }{ 2 } \)

(b)

\(\sqrt { \frac { 1 }{ 3 } } \)

(c)

\(\sqrt { \frac { 2 }{ 3 } } \)

(d)

\(\sqrt { \frac { 3 }{ 2 } } \)

The difference of the focal distances of any point on the hyperbola is equal to ______.

1

(a)

length of conjugate axis

(b)

length of transverse axis

(c)

latus rectum

(d)

none of these

The latus rectum of the hyperbola \({ 16x }^{ 2 }-{ ay }^{ 2 }=144\quad is\) _______.

1

(a)

323

(b)

\(\frac { 15 }{ 4 } \)

(c)

\(\frac { 4 }{ 3 } \)

(d)

\(\frac { 3 }{ 4 } \)