The equation y 2 - 8y - x + 19 = 0 represents

a parabola whose vetex is (3,and directrix is x = 11/4

a parabola whose focus is (1/4,and directrix is x = -1/4

a parabola whose focus is (13/4,and vertex is (0, 0)

a curve which is not a parabola

JEE Questions for Maths Conic Section Quiz 3

A hyperbola passes through (3,and the length of its conjugate axis is 8. The length of latusrectum is

0%
20/3
0%
40/3
0%
50/3
0%
None of these

The equation y² + 4x + 4y + k = 0 represents a parabola whose latusrectum is

0%
1
0%
2
0%
3
0%
4

If (x, y) are any point on the parabola y² = 4x. Let P be the point that divides the line segment from (0,to (x, y) in the ratio 1 : 3. Then, the locus of P is

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x2 = y
0%
y2 = 2xy
0%
y2 = x
0%
x2 = 2y

If the centre, one of the foci and semi - major axis of an ellipse are (0, 0), (0,and 5, then its equation is

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

The straight lines y = ± x intersect the parabola y² = 8x in points P and Q, then length of PQ is

0%
4
0%
4√2
0%
8
0%
16

The sum of the reciprocals of focal distance of a focal chord PQ of y² = 4ax is

0%
1/a
0%
a
0%
2a
0%
1/2a

The length of the latusrectum of the ellipse 16x² + 25y² = 400 is

0%
5/6 units
0%
32/5 units
0%
16/5 units
0%
5/32 units

The eccentricity of the hyperbola with latusrectum 12 and semi - conjugate axis 2√3 is

0%
3
0%
2)
0%
2√3
0%
2

If t₁ and t₂ are the parameters of the end points of a focal chord for the parabola y² = 4ax, then which one is correct

0%
t1 t2 = 1
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t1/ t2 = 1
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t1 t2 = - 1
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t1 + t2 = 1

The distance between the foci of the conic 7x² – 9y² = 63 is equal to

0%
8
0%
4
0%
3
0%
7
0%
12

One of the points on the parabola y² = 12x with focal distance 12 is

0%
(3, 6)
0%
(9, 6√3)
0%
(7, 2√21)
0%
(8, 4√6)

0%
25
0%
9
0%
4
0%
5
0%
16

If the length of the major axis of an ellipse is 7/18 times the length of the minor axis, then eccentricity of the ellipse is

0%
8/17
0%
15/17
0%
9/17
0%
2√2/17
0%
13/17

S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, then the eccentricity of the ellipse is

0%
1/4
0%
1/3
0%
1/2
0%
2/3

The distance of a point P on the parabola y² = 12x, if the ordinate of P is 6, is

0%
12
0%
6
0%
3
0%
9

The sum of the distance of a point (2, -from the foci of an ellipse 16(x - 2)² + 25(y + 3)² = 400 is

0%
8
0%
6
0%
50
0%
32
0%
10

0%
16/7
0%
25/4
0%
25/12
0%
16/9
0%
23/16

The coordinates of the focus of the parabola described parametrically by x = 5t² + 2, y = 10t + 4 are

0%
(7, 4)
0%
(3, 4)
0%
(3, -4)
0%
(-7, 4)

In an ellipse, if the lines joining focus to the extremities of the minor axis from an equilateral triangle with the minor axis, then the eccentricity of the ellipse is

0%
√3/2
0%
√3/4
0%
1/√2
0%

Equation of the directrix of parabola 2x² = 14y is equal to

0%
y = - (7/4)
0%
x = - (7/4)
0%
y = (7/4)
0%
x= (7/4)

The equation y² - 8y - x + 19 = 0 represents

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a parabola whose focus is (1/4,and directrix is x = -1/4
0%
a parabola whose vetex is (3,and directrix is x = 11/4
0%
a parabola whose focus is (13/4,and vertex is (0, 0)
0%
a curve which is not a parabola

If in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latusrectum is

0%
9
0%
9/2
0%
32/3
0%
64/3

If I denotes the semi - latusrectum of the parabola y² = 4ax and SP and SQ denote the segments of any focal chord PQ, S being the focus, then SP, I and SQ are in the relation

0%
AP
0%
GP
0%
HP
0%
I2 = SP2 + SQ2

A parabola has the origin as its focus and the line x = 2 as the directrix. Then, the vertex of the parabola is at

0%
(2, 0)
0%
(0, 2)
0%
(1, 0)
0%
(0,

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2, the length of semi - major axis is

0%
5/3
0%
8/3
0%
2/3
0%
4/3

0%
√2 : 1
0%
√3 : √2
0%
1 : 2
0%
2 : 1

The focal distance of a point on the parabola y² = 16x, whose ordinate is twice the abscissa, is

0%
6
0%
8
0%
10
0%
12

0%
4
0%
3/7
0%
√12
0%
7/2

If e₁ and e₂ are the eccentricities of a hyperbola 3x² - 3y² = 25 and its conjugate, then

0%
e21 + e22 = 2
0%
e21 + e22 = 4
0%
e1 + e2 = 4
0%
e1 + e2 = √2

A conic section is defined by the equations x = - 1 + sect, y = 2 + 3 tan t.The coordinates of the foci are

0%
(-1 - √10,and (-1 + √10, 2)
0%
(-1 - √8,and (-1 + √8, 2)
0%
(-1, 2- √and (-1, 2 + √8)
0%
(√10,and (-√10, 0)

0%
- (√3/2)
0%
1/2
0%
√5/2
0%
√7/ 3
0%
√3

The vertex of the parabola x² + 2y = 8x - 7 is

0%
(9/2, 0)
0%
(4, 9/2)
0%
(2, 9/2)
0%
(4, 7/2)

Eccentricity of the ellipse x² + 2y² - 2x + 3y + 2 = 0 is

0%
1/√2
0%
1/2
0%
1/2√2
0%
1/√3

The sum of the focal distances from any point on the ellipse 9x² + 16y² = 144 is

0%
3
0%
6
0%
8
0%
4

0%
a2 = 16, b2 = 12
0%
a2 = 12, b2 = 16
0%
a2 = 16, b2 = 4
0%
a2 = 4,b2 = 16

If OAB is an equilateral triangle inscribed in the parabola y² = 4ax with O as the vertex, then the length of the side of ∆OAB is

0%
8a√3
0%
4a√3
0%
2a√3
0%
a√3

One of the directrices of the ellipse 8x² + 6y² - 16x + 12y + 13 = 0 is

0%
3y - 3 = √6
0%
3y + 3 = ±√6
0%
y + 1 = √3
0%
y - 1 = - √3

Equation of the latusrectum of the ellipse 9x² + 4y² - 18x - 8y - 23 = 0

0%
y = ±√5
0%
y = -√5
0%
y = 1 ± √5
0%
χ = -1± √5

Statement I the curve y = - (x²/+ x + 1 is symmetric with respect to the line x = 1.
Statement II A parabola is symmetric about its axis

0%
Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I
0%
Statement I is correct, Statement II is correct; Statement II is not correct explanation for Statement I
0%
Statement I is correct, Statement II is incorrect
0%
Statement I is incorrect, Statement II is correct