JEE Questions for Maths Conic Section Quiz 14

The locus of the point of intersection of lines (x + y)t = a and x – y = at, where t is the parameter, is

0%
A circle
0%
An ellipse
0%
A rectangular hyperbola
0%
None of these

The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is 16 and eccentricity is √2 is

0%
0%
2)
0%
0%

0%
1
0%
5
0%
7
0%
9

0%
0%
2)
0%
0%
None of these

0%
Parabola
0%
Rectangular hyperbola
0%
Hyperbola
0%
Ellipse

The reciprocal of the eccentricity of rectangular hyperbola, is

0%
2
0%
2)
0%
0%

0%
9
0%
4
0%
5
0%
1

If transverse and conjugate axes of a hyperbola are equal, then its eccentricity

0%
0%
2)
0%
0%
2

0%
5
0%
4
0%
–5
0%
None of these

0%
0%
2)
0%
0%

0%
Centre only
0%
Centre, foci and directories
0%
Centre, foci and vertices
0%
Centre and vertices only

0%
192
0%
64
0%
16
0%
32

0%
A hyperbola if k > 8
0%
An ellipse if k > 8
0%
A hyperbola if 8 < k < 12
0%
None of the above

0%
(–6, 3)
0%
(6, 3)
0%
(6, 3)
0%
(6, –3)
0%
(√24, 0)

The equation of a hyperbola whose asymptotes are 3x ± 5y = 0 and vertices are (±5,is

0%
0%
2)
0%
0%

0%
No locus if k > 0
0%
An ellipse, if k > 0
0%
A point if, k = 0
0%
A hyperbola, if k > 0

The number of points of intersection of the two curves y = 2sinx and y = 5x² + 2x + 3 is

0%
0
0%
1
0%
2
0%
∞

0%
0%
2)
0%
0%

The locus of the midpoint of the line segment joining the focus to a moving point on the parabola on the parabola y² = 4ax is another parabola with the directrix

0%
x = –a
0%
x = –a/2
0%
x = 0
0%
x = a/2

0%
(1, 1)
0%
(1, 0)
0%
(1, –1)
0%
(0, 0)

0%
0%
2)
0%
0%

0%
1/8
0%
8
0%
4
0%
1/4

The centre of the circle passing through the point (0,and touching the curve y = x² at (2,is

0%
0%
2)
0%
0%
None of these

0%
0%
2)
0%
0%

Which one of the following curves cuts the parabola y² = 4ax at right angles

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

The locus of mid point of that chord of parabola which subtends right angle on the vertex will be

0%
0%
2)
0%
0%

The equation of a circle passing through the vertex and the extremities of the latus rectum of the parabola y² = 8x is

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%
1

0%
ab
0%
abe
0%
0%

A man running round a race-course notes that the sum of the distance of two flsh-posts from him is always 10 metres and the distance between the flag-posts is 8 metres. The area of the path he encloses in square metres is

0%
0%
2)
0%
0%

If the angle between the lines joining the end points of minor axis of an ellipse with its foci is π/2, then the eccentricity of the ellipse is

0%
0%
2)
0%
0%

The eccentricity of an ellipse, with its centre at the origin, is ½. If one of the directrices is x = 4, then the equation of the ellipse is

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%
None of the above

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

The locus of the middle point of the intercepts of the tangents drawn from an external point to the ellipse x² + 2y² = 2 between the coordinates axes is