JEE Questions for Maths Conic Section Quiz 6 - MCQExams.com

The locus of a point P(α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola
Maths-Conic Section-17299.png
  • a hyperbola
  • a parbola
  • a circle
  • an ellipse

Maths-Conic Section-17300.png
  • 4x - 3y = ± 6√5
  • 4x - 3y = ± √12
  • 4x - 3y = ± √2
  • 4x - 3y = ± 1
The slope of tangents drawn from a point (4,to the parabola y2 = 9x, are

  • Maths-Conic Section-17301.png
  • 2)
    Maths-Conic Section-17302.png

  • Maths-Conic Section-17303.png
  • None of these
The angle between the tangents drawn from the point (1,to the parabola y2 = 4x is
  • π/6
  • π/4
  • π/3
  • π/2
The number of maximum normals which can be drawn from a point to ellipse is
  • 4
  • 2
  • 1
  • 3
The value of m, for which the line y = mx + 2 becomes a tangent to the conic 4x2 - 9y2 = 36, are

  • Maths-Conic Section-17304.png
  • 2)
    Maths-Conic Section-17305.png

  • Maths-Conic Section-17306.png

  • Maths-Conic Section-17307.png
If the parabola y2 = 4ax passes through the point (1, -2), then tangent at this point is
  • x - y - 1 = 0
  • x + y + 1 = 0
  • x - y + 1 = 0
  • None of these
The line among the following which touches the parabola y2 = 4ax, is
  • x + my + am3 = 0
  • x - my + am2 = 0
  • x + my - am2 = 0
  • y + mx + am2 = 0
From the point (-1, -two tangents are drawn to the parabola y2 = 4x. Then, the angle between the two tangents is
  • 30o
  • 45o
  • 60o
  • 90o
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axes at C. The projection of BC on the axis of the parabola is
  • 2
  • 2a
  • 4a
  • 8a

Maths-Conic Section-17309.png
  • focus
  • centre
  • end of the major axis
  • end of the minor axis
The equation of the director circle of the hyperbola 9x - 16y2 = 144 is
  • x2 + y2 = 7
  • x2 + y2 = 9
  • x2 + y2 = 16
  • x2 + y2 = 25
If P(at2, 2at) is one end of a focal of the parabola y2 = 4ax, then the length of the focal chord is

  • Maths-Conic Section-17310.png
  • 2)
    Maths-Conic Section-17311.png

  • Maths-Conic Section-17312.png

  • Maths-Conic Section-17313.png
Locus of mid - point of any focal chord y2 = 4ax is
  • y2 = a(x - 2a)
  • y2 = 2a(x - 2a)
  • y2 = 2a(x - a)
  • None of these
The equation of the chord joining two points (x 1, y1) and (x 2, y2) on the rectangular hyperbola xy = c2 is

  • Maths-Conic Section-17315.png
  • 2)
    Maths-Conic Section-17316.png

  • Maths-Conic Section-17317.png

  • Maths-Conic Section-17318.png
Find the measure of angle between the asymptotes of x2 - y2 = 16
  • π/4
  • π/3
  • π/6
  • π/2
The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x2 + 9y2 = 9 meets its auxiliary circle at the point M. Then, the area of the triangle with vertices A, M and the origin O is
  • 31/10
  • 29/10
  • 21/10
  • 27/10
The product of perpendicular drawn from any point of a hyperbola to its asymptotes is

  • Maths-Conic Section-17319.png
  • 2)
    Maths-Conic Section-17320.png

  • Maths-Conic Section-17321.png

  • Maths-Conic Section-17322.png
Given the two ends of the latus rectum, the maximum number of parabolas that can be drawn is
  • 1
  • 2
  • 0
  • infinite
If the vertex of the parabola is (2,and extremities of the latus rectum are (3,and (3,–2), then the equation of the parabola is
  • y2 = 2x ‒ 4
  • y2 = 4y ‒ 8
  • y2 = 4x ‒ 8
  • none of these.
The equation of the parabola whose vertex and focus are on the positive side of the x–axis at distances α and b respectively from the origin is
  • y2 = 4 (b ‒ a)(x ‒ a)
  • y2 = 4 (a ‒ b)(x ‒ b)
  • x2 = 4 (b ‒ a)(y ‒ a)
  • none of these
A line L passing thro’ the focus of the parabola y2 = 4(x –intersects the parabola in two distinct points. If ‘m’ be the slope of the line L, then
  • –1 < m < 1
  • m < –1 or m > 1
  • m∈R – {0}
  • none of these
The length of a focal chord of the parabola y2 = 4ax at a distance b from the vertex is C. Then
  • 2 a2 = bc
  • a3 = b2c
  • ac = b2
  • b2c = 4a3

Maths-Conic Section-17328.png
  • t2 = 2t1
  • t2 = 2t1 = 0
  • t1+ 2t2 = 0
  • none of these
The number of points with integral co – ordinates that lie in the interior of the region common to the circle x2 + y2 = 16 and the parabola y2 = 4x is
  • 8
  • 10
  • 18
  • none of these
The number of distinct normals that can be drawn from (–2,to the parabola y2 – 4x – 2y – 3 = 0 is
  • 1
  • 2
  • 3
  • 0
If two of the three feet of normals drawn from a point to the parabola y2 = 4x be (1,and (1, –2), then the third foot is

  • Maths-Conic Section-17332.png
  • 2)
    Maths-Conic Section-17333.png
  • (0,0)
  • none of these
The A.M. of the ordinates of the feet of the normals from (3,to the parabola y2 = 8x is
  • 4
  • 0
  • 8
  • none of these
The circle x2 + y2 + 2λx = 0, λ ∈ R, touches the parabola y2 = 4x externally. Then
  • λ > 0
  • λ < 0
  • λ > 1
  • none of these
If the vertex and the focus of the parabola are (–1,and (2,respectively, then the equation of the directrix is
  • 3x + 2y + 14 = 0
  • 3x + 2y ‒ 25 = 0
  • 2x ‒ 3y + 10 = 0
  • none of these
The point (a, 2a) is an interior point of the region bounded by the parabola y2 = 16x and the double ordinate thro’ the focus. Then
  • a < 4
  • 0 < a < 4
  • 0 < a < 2
  • a > 4
If two tangents drawn from the point (α, β) to the parabola y2 = 4x be such that the slope of one tangent is double of the other, then

  • Maths-Conic Section-17339.png
  • 2)
    Maths-Conic Section-17340.png

  • Maths-Conic Section-17341.png
  • none of these.
y + h = m1(x + a) and y + k = m2 (x + a) are two tangents to the parabola y2 = 4ax ; then
  • m1 + m2 = 0
  • m1 m2 = 1
  • m1 m2 = −1
  • none of these
The area of the triangle formed by the tangent and the normal to the parabola y2 = 4ax, both drawn at the same end of the latus rectum and the axis of the parabola is

  • Maths-Conic Section-17343.png
  • 2a2
  • 4a2
  • none of these
Let P, Q, R be three pts. on a parabola, normals at which are concurrent. The centroid of the ∆ PQR must lie on
  • a line parallel to the directrix
  • the axis of the parabola
  • a line of slope 1 passing thro’ the vertex
  • none of these
The vertex of the parabola y2 = 8x is at the centre of a circle and the parabola cuts the circle at the ends the latus rectum. Then the equation of the circle is
  • x2 + y2 = 4
  • x2 + y2 = 20
  • x2 + y2 = 80
  • none of these
If O is the pole of the chord PQ of a parabola, then the perpendicular from P, O, Q on any tangent to the curve are in
  • A.P.
  • G.P.
  • H.P.
  • none of these
The ends of a line segment are P (1,and Q (1, 1). R is a point on the line segment PQ such that PR : RQ = 1 : λ. If R is an interior point of the parabola y2 = 4x , then
  • λ ∈ (0, 1)
  • 2)
    Maths-Conic Section-17348.png

  • Maths-Conic Section-17349.png
  • none of these.

Maths-Conic Section-17351.png
  • A hyperbola
  • An ellipse
  • A pair of straight lines
  • A rectangular hyperbola

Maths-Conic Section-17353.png
  • (2, 3)
  • (2, –3)
  • (–2, 3)
  • (–2, –3)
The equation of the conic with focus at (1, –1), directrix along x – y = 0 and with eccentricity √2 is

  • Maths-Conic Section-17355.png
  • 2)
    Maths-Conic Section-17356.png

  • Maths-Conic Section-17357.png

  • Maths-Conic Section-17358.png

Maths-Conic Section-17360.png

  • Maths-Conic Section-17361.png
  • 2)
    Maths-Conic Section-17362.png

  • Maths-Conic Section-17363.png

  • Maths-Conic Section-17364.png

Maths-Conic Section-17366.png
  • Parabola
  • Ellipse
  • Ellipse
  • Pair of straight lines

Maths-Conic Section-17368.png

  • Maths-Conic Section-17369.png
  • 2)
    Maths-Conic Section-17370.png

  • Maths-Conic Section-17371.png
  • None of these
If a double ordinate of the parabola y2 = 4ax be of length 8a, the the angle between the lines joining the vertex of the parabola of the ends of this double ordinate is
  • 30o
  • 60o
  • 90o
  • 120o
PQ is a double ordinate of the parabola y2 = 4ax. The locus of the points of transaction of PQ is

  • Maths-Conic Section-17374.png
  • 2)
    Maths-Conic Section-17375.png

  • Maths-Conic Section-17376.png

  • Maths-Conic Section-17377.png
If the vertex of a parabola be at origin and directrix be x + 5 = 0, then its latus rectum is
  • 5
  • 10
  • 20
  • 40
The latus rectum of a parabola whose directrix is x + y – 2 = 0 and focus is (3, –is

  • Maths-Conic Section-17380.png
  • 2)
    Maths-Conic Section-17381.png

  • Maths-Conic Section-17382.png

  • Maths-Conic Section-17383.png
The equation of the lines joining the vertex of the parabola y2 = 6x to the points on it whose abscissa is 24 is
Maths-Conic Section-17385.png
  • b and c
  • b and d
  • only a
  • only b
Let (x, y) be 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

  • Maths-Conic Section-17387.png
  • 2)
    Maths-Conic Section-17388.png

  • Maths-Conic Section-17389.png

  • Maths-Conic Section-17390.png
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Maths Quiz Questions and Answers