Conic Section Quiz-13

Conic Section Quiz-13

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. 

•  (2, 5/2)
•  Data are not sufficient
•  (-2,-5/2)
•  Data are inconsistent

Solution

Q2. Minimum radius of circle which is orthogonal with both the circles x²+y²-12x+35=0 and x²+y²+4x+3=0 is

•  4
•  3
•  √15
•  1

Solution

Q3. If one of the diameters of the circle x²+y²-2x-6y+6=0 is a chord to the circle with centre (2, 1), then the radius of the circle is

•  √3
•  √2
•  3
•  2

Solution

Q4.   Let any double ordinate PNP' of the hyperbola x²/25+y²/16=1 be produced on both sides to meet the asymptotes in Q and Q', then PQ∙P'Q is equal to

•  25
•  16
•  41
•  None of these

Solution

Q5. If (0,6)and (0,3) are respectively the vertex and focus of a parabola, then its equation is

•  x²+12y=72
•  x²-12y=72
•  y²-12x=72
•  y²+12x=72

Solution

Q6. P is a point on the hyperbola x²/a² -y²/b² =1, N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, the OT. ON is equal to

•  e²
•  a²
•  b²
•  b²/a²

Solution

Q7. If the locus of middle of point of contact of tangent drawn to the parabola y²=8x and foot of perpendicular drawn from its focus to the tangents is a conic then length of latus rectum of this conic is

•  9/4
•  9
•  18
•  9/2

Solution

Q8. Consider the parabola y²=4x. A≡(4,-4) and B≡(9,6) be two fixed points on the parabola. Let ‘C’ be a moving point on the parabola between A and B such that the area of the triangle ABC is maximum, then coordiante of ‘C’

•  (1/4,1)
•  (4, 4)
•  (3,2√3)
•  (3,-2√3)

Solution

Q9.If O is the origin and OP,OQ are the tangents from the origin to the circle x²+y²-6x+4y+8=0, then circumcenter of the triangle OPQ is

•  (3,-2)
•  (3/2,-1)
•  (3/4,-1/2)
•  (-3/2,1)

Solution

Q10.A straight line moves such that the algebraic sum of the perpendicular drawn to it from two fixed points is equal to 2k. Then , the straight line always touches a fixed circle of radius

•  2k
•  k/2
•  k
•  None of these