## Conic Section Quiz-17

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. Two mutually perpendicular tangent of the parabola y2=4ax meet the axis in P1 and P2. If S is the focus of the parabola, then 1/(SP1))+1/(SP2)) is equal to
•  4/a
•  2/a
•  1/a
•  x=1/4a
Solution
Q2. If the vertex of a hyperbola bisects the distance between its centre and the corresponding focus, then ratio of square of its conjugate axis to the square of its transverse axis is
•  2
•  4
•  6
•  3
Solution
Q3. If the line ax+by=2 is a normal to the circle x2+y2-4x-4y=0 and a tangent to the circle x2+y2=1, then
•  a=1/2,b=1/2>
•  a=(1+√7)/2,b=(1-√7)/2
•  a=1/4,b=3/4
•  a=1,b=√3
Solution

Q4.   From point P(8,27) tangent PQ and PR are drawn to the ellipse x2/4+y2/9=1. Then the angle subtended by QR at origin is
•  tan-1⁡√6/65
•  tan-1 (4√6)/65
•  tan-1(8√2)/65
•  tan-1(48√6)/455
Solution
Q5. Two straight lines are perpendicular to each other. One of them touches the parabola y2=4a(x+a) and the other touches y2=4b(x+b). Their point of intersection lies on the line
•  x-a+b=0
•   x+a-b=0
•  x+a+b=0
•  x-a-b=0
Solution
Q6. P,Q,R are the feet of the normals drawn to a parabola (y-3)2=8(x-2). A circle cuts the above parabola in points P,Q,R and S. Then this circle always passes through the point
•  (2, 3)
•  (3, 2)
•   (0, 3)
•  (2, 0)
Solution
Q7. Let ‘C’ be a curve which is locus of the point of the intersection of lines x=2+m and my=4-m. A circle s≡(x-2)2+(y+1)2= 25 intersects the curve C at four points P,Q,R and S. If O is centre of the curve ‘C’ then OP2+OQ2+OR2+OS2 is
•  50
•  100
•  25
•  25/2
Solution
Q8. The locus of the centre of the circles such that the point (2,3) is the midpoint of the chord 5x+2y=16 is
•  2x-5y+11=0
•  2x+5y-11=0
•  2x+5y+11=0
•  None
Solution
Q9.If the segment intercepted by the parabola y=4ax with the line lx+my+n=0 subtends a right angle at the vertex, then
•  4al+n=0
•  4al+4am+n=0
•  4am+n=0
•  al+n=0
Solution
Q10.If S and S’ are the foci of the ellipse x2/25+y2/3=1, and P is any point on it then range of values of SP.S’P is
•  9≤f(Î¸)≤16
•  9≤f(Î¸)≤25
•  16≤f(Î¸)≤25
•   1≤f(Î¸)≤16

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Conic Section Quiz-17