Conic Section Quiz-17

Conic Section Quiz-17

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. 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(θ)≤16
•  9≤f(θ)≤25
•  16≤f(θ)≤25
•   1≤f(θ)≤16