## Conic Section Quiz-32

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 point of intersection of the tangents of the parabola y^2=4x, drawn at end points of the chord x+y=2 lies on
•   x-2y=0
•   x+2y=0
•   y-x=0
•   x+y=0
Solution
Q2.  If the eccentricity of the hyperbola x^2-y^2 sec^2 Î±=5 is √3 times the eccentricity of the ellipse x^2 sec^2 Î±+y^2=25, then a value of Î± is
•  Ï€/6
•  Ï€/4
•  Ï€/3
•  Ï€/2
Q3.  Tangents are drawn to the circle x^2+y^2=1 at the points where it is met by the circles, x^2+y^2=(Î»+6)x+(8-2Î»)y-3=0,Î» being the variable. The locus of the point of intersection of these tangents is
•   2x-y+10=0
•   x+2y-10=0
•   x-2y+10=0
•   2x+y-10=0
Solution

Q4.
At what point on the parabola y^2=4x the normal makes equal angle with axes?
•   (4, 4)
•   (9, 6)
•   (4,-4)
•   (1,±2)
Solution
Q5.  The angle between the tangents to the parabola y^2=4ax at the points where it intersects with the line x-y-a=0 is
•  Ï€/3
•  Ï€/4
•  Ï€/6
•  Ï€/2
Solution
Q6.  Let ABCD be a quadrilateral with are 18, with side AB parallel to the side CD and AB=2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the side, then its radius is
•   3
•   2
•   3/2
•   1
• Solution
Q7.  min [(x_1-x_2 )^2+(5+√(1-x_1^2 )-√(4x_2 ))^2 ]∀ x_1,x_2∈R is
•   √5+1
•   4√5-1
•  √5+1
•   √5-1
2x^2-2y^2+5xy+5=0
Q8.  The locus of the vertex of the family of parabolas y=(a^3 x^2)/3+(a^2 x)/2-2a is
•  xy=105/64
•  xy=3/4
•  xy=35/16
•  xy=64/105
Solution
Q9. The two circles which passes through (0,a) and (0,-a) and touch the line y=mx+c will intersect each other at right angle, if
•   a^2=c^2 (2m+1)
•   a^2=c^2 (2+m^2 )
•   c^2=a^2 (2+m^2 )
•   c^2=a^2 (2m+1)
Solution
Q10. If the normals to the parabola y^2=4ax at the ends of the latus rectum meet the parabola at Q,Q', then QQ' is
•  10a
•  4a
•  20a
•  12a
Solution

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Conic Section Quiz-32