Conic Section Quiz-34

Conic Section Quiz-34

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.  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 α for which the line 2y=gx+α 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