## Conic Section Quiz-36

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 Î± for which the point (Î±,1) lies inside the curves c_1:x^2+y^2-4=0 and c_2:y^2=4x is
•  |Î±|gt√3
•  |Î±|gt2
•  1/4gtÎ±gt√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 Î»(0gtÎ»gt1) 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
•   2Î»
•   2Î»/(-1+Î»^2 )
•   (1-Î»^2)/(1+Î»^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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