Conic Section Quiz-30

Conic Section Quiz-30

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.  Normals drawn to y^2=4ax at the points where it is intersected by the line y=mx+c intersect at P. Foot of the another normal drawn to the parabola from the point ‘P’ is

•   (a/m^2 ,-2a/m)
•   (9a/m,(-6a)/m)
•   (am^2,-2am)
•   (4a/m^2 ,-4a/m)

Solution

Q2.  If y=m_1 x+c and y=m_2 x+c are two tangents to the parabola y^2+4a(x+a)=0, then

•  m1+m2=0
•  1+m1+m2=0
•  m_1 m_2-1=0
•  1+m_1m_2=0

Q3.  If tangents OQ and OR are dawn to variable circles having radius r and the centre lying on the rectangular hyperbola xy=1, then locus of circumcentre of triangle OQR is (O being the origin)

•   xy=4
•   xy=1/4
•   xy=1
•   None of these

Solution

Q4.    Locus of the point which divides double ordinates of the ellipse x^2/a^2 +y^2/b^2 =1 in the ratio 1:2 internally is

•   x^2/a^2 +(9y^2)/b^2 =1
•   x^2/a^2 +(9y^2)/b^2 =1/9
•   (9x^2)/a^2 +(9y^2)/b^2 =1
•   None of these

Solution

Q5.  C is the centre of the circle with centre (0,1) and radius unity. P is the parabola y=ax^2. The set of values of ‘a’ for which they meet at a point other than the origin, is

•  a>0
•  a∈(0,1/2)
•  (1/4,1/2)
•  (1/2,∞)

Solution

Q6.  If the normals at points ‘t_1’ and ‘t_2’ meet on the parabola, then

•   t_1 t_2=-1
•   t_2=-t_1-2/t_1
•   t_1 t_2=2
•   None of these
Solution

Q7.  If foci of hyperbola lie on y=x and one of the asymptote is y=2x, then equation of the hyperbola, given that it passes through (3, 4) is

•   x^2-y^2-5/2 xy+5=0
•   2x^2-2y^2+5xy+5=0
•  2x^2-2y^2+5xy+5=0
•   None of these

2x^2-2y^2+5xy+5=0

Q8.  The value of ‘c’ for which the set {(x,y)|x^2+y^2+2x≤1}⋂{(x,y)|x-y+c≥0} contains only one point on common is

•  (-∞,-1]∪[3,∞)
•  {-1,3}
•  {-3}
•  {-1}

Solution

Q9. If two different tangents of y^2=4x are the normals to x^2=4by then

•   |b|>1/(2√2)
•   |b|gt1/(2√2)
•   |b|> 1/√2
•   |b|gt1/√2

Solution

Q10. The normal at the point P(ap^2,2ap) meets the parabola y^2=4ax again at Q(aq^2,2aq) such that the lines joining the origin to P and Q are at right angle. Then

•  p^2=2
•  q^2=2
•  p=2q
•  q=2p

Solution