## Conic Section Quiz-34

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.  Locus of the midpoint of any normal chords of y^2=4ax is
•   x=a((4a^2)/y^2 -2+y^2/(2a^2 ))
•   x=a((4a^2)/y^2 +2+y^2/(2a^2 ))
•   x=a((4a^2)/y^2 -2-y^2/(2a^2 ))
•   x=a((4a^2)/y^2 +2-y^2/(2a^2 ))
Solution
Q2.  If the chord of contact of tangents from a point P to a given circle passes through Q, then the circle on PQ as diameter
•  Cuts the given circle orthogonally
•  Touches the given circle externally
•  Touches the given circle internally
•  None of these
Q3.  The locus of the foot of the perpendicular form the centre of the hyperbola xy=1 on a variable tangent is
•   〖(x^2-y^2)〗^2=4xy
•   〖(x^2+y^2)〗^2=2xy
•   (x^2+y^2)=4xy
•   〖(x^2+y^2)〗^2=4xy
Solution

Q4.
The locus of the midpoints of the chords of the circle x^2+y^2-ax-by=0 which subtend a right angle at (a/2,b/2) is
•   ax+by=0
•   ax+by=a^2+b^2
•   x^2+y^2-ax-by+(a^2+b^2)/8=0
•   x^2+y^2-ax-by-(a^2+b^2)/8=0
Solution
Q5.  The range of values of Î± for which the line 2y=gx+Î± is a normal to the circle x^2+y^2+2gx+2gy-2=0 for all values of g is
•  [1,∞)
•  [-1,∞)
•  (0, 1)
•  (-∞,1]
Solution
Q6.  Consider a circle x^2+y^2+ax+by+c=0 lying completely in first quadrant. If m_1 and m_2 are the maximum and minimum values of y/x for all ordered pairs (x,y) on the circumference of the circle, then the value of (m_1+m_2) is
•   (a^2-4c)/(b^2-4c)
•   2ab/(b^2-4c)
•   2ab/(4c-b^2 )
•   2ab/(b^2-4ac)
• Solution
Q7.  The chord of contact of tangents from a point P to a circle passes through Q. If I_1 and I_2 are the lengths of the tangents from P and Q to the circle, then PQ is equal to
•   (I_1+I_2)/2
•   (I_1-I_2)/2
•  √(I_1^2+I_2^2 )
•   2√(I_1^2+I_2^2 )
Q8.  If S=0 be the equation of the hyperbola x^2+4xy+3y^2-4x+2y+1=0, then the value of k for which S+K=0 represents its asymptotes is
•  20
•  -16
•  -22
•  18
Solution
Q9. If angle between asymptotes of hyperbola x^2/a^2 -y^2/b^2 =1 is 120° and product of perpendiculars drawn from foci upon its any tangent is 9, then locus of point of intersection of perpendicular tangents of the hyperbola can be
•   x^2+y^2=6
•   x^2+y^2=9
•   x^2+y^2=3
•   x^2+y^2=18
Solution
Q10. If bisector of the angle APB, where PA and PB are the tangents to the parabola y^2=4ax, is equally inclined to the coordinate axes, then the point P lies on
•  Tangent at vertex of the parabola
•  Directrix of the parabola
•  Circle with centre at the origin and radius a
•  The line of latus rectum
Solution

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Conic Section Quiz-34