## Conic Section Quiz-30

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

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Conic Section Quiz-30