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Conic Section Quiz-36

Dear Readers,

In JEE exams, Conic section is one of the most important topic of Mathematics that comes under Coordinate Geometry, it has total of 15 percent weightage out of which 6% questions are asked in JEE mains and 9% in Advance.

Q1.  The coordinates of the middle point of the chord cut-off by 2x-5y+18=0 by the circle x^2+y^2-6x+2y-54=0 are
  •   (1, 4)
  •   (2, 4)
  •   (4, 1)
  •   (1, 1)
Solution
Q2.  Set of values of α for which the point (α,1) lies inside the curves c_1:x^2+y^2-4=0 and c_2:y^2=4x is
  •  |α|gt√3
  •  |α|gt2
  •  1/4gtαgt√3
  •  None of these
Q3.  The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant, is a/an
  •   Parabola
  •   Circle
  •   Ellipse
  •   Straight Line
Solution

Q4.   
A line of slope λ(0gtλgt1) touches parabola y+3x^2=0 at P. If S is the focus and M is the foot of the perpendicular of directrix from P, then tan ∠MPS equals
  •   2λ
  •   2λ/(-1+λ^2 )
  •   (1-λ^2)/(1+λ^2 )
  •   None of these
Solution
Q5.  A circle has the same centre as an ellipse and passes through the foci F_1 and F_2 of the ellipse, such that the two curves intersect in 4 points. Let 'P' be any one of their point of intersection. If the major axis of the ellipse is 17 and the area of the triangle PF_1 F_2 is 30, then the distance between the focii is
  •  13
  •  10
  •  11
  •  None of these
Solution
Q6.  Number of points on the hyperbola x^2/a^2 -y^2/b^2 =3, from which mutually perpendicular tangents can be drawn to the circle x^2+y^2=a^2, is/are
  •   0
  •   2
  •   3
  •   4
  • Solution
Q7.  The equation of the circle passing through the point of intersection of the circle x^2+y^2=4 and the line 2x+y=1 and having minimum possible radius is
  •   5x^2+5y^2+18x+6y-5=0
  •   5x^2+5y^2+9x+8y-15=0
  •  5x^2+5y^2+4x+9y-5=0
  •   5x^2+5y^2-4x-2y-18=0
Q8.  The length of the transverse axis of the rectangular hyperbola xy=18 is
  •  6
  •  12
  •  18
  •  9
Solution
Q9. Consider a family of circle which are passing through the point (-1,1) and are tangent to x-axis. If (h,k) are the coordinates of the centre of the circles, then the set of values of k given by the interval
  •   k≥1/2
  •   -1/2≤k≤1/2
  •   k≤1/2
  •   0 gt k gt 1/2
Solution
Q10. If a≠0 and the line 2bx+3cy+4d=0 passes through the points of intersection of the parabola y^2=4ax and x^2=4ay, then
  •  d^2+(2b+3c^ )^2=0
  •  d^2+(3b+2c)^2=0
  •  d^2+(2b-3c)^2=0
  •  None of these
Solution


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