Conic Section Quiz-16

Conic Section Quiz-16

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. Which one of the following equations represented parametrically equation to a parabolic curve

•  x=3 cos⁡t;y=4 sin⁡t
•  x²-2=2 cos⁡t;y=4 cos²⁡t/2
•  √x= tan⁡t; √y =sec⁡t
•  x= √(1-sin⁡t ) ; y=sin⁡t/2+cos⁡t/2

Solution

Q2. The latus rectum of the hyperbola 9x²-16y²-18x-32y-151=0 is

•  9/4
•  9
•  3/2
•  9/2

Solution

Q3. Parabolas y²⁡=4a(x-c1 ) and x²⁡=4a(y-c2 ), where c1and c2 are variable, are such that they touch each other. Locus of their point of contact is

•  xy=2a²
•  xy=4a²
•  xy=a²
•  None of these

Solution

Q4.   Let d1 and d2 be the lengths of the perpendicular drawn from foci S and S' of the ellipse x²⁡/a²⁡ +y²⁡/b²⁡ =1 to the tangent at any point Pon the ellipse. Then, SP:S'P=

•  d1:d2
•  d2:d1
•  d1²:d2²
•  √(d1 )/√(d2 )

Solution

Q5. The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x²+9y²=9 meets its auxiliary circle at the point M. Then, the area of the triangle with vertices at A,M and the origin O is

•  31/10
•  29/10
•  21/10
•  27/10

Solution

Q6. If the tangent at the point P(2,4) to the parabola y²=8x meets the parabola y²=8x+5 at Q and R then the midpoint of QR is

•  (4, 2)
•  (2, 4)
•  (7, 9)
•  None of these

Solution

Q7. A circle of constant radius 'a' passes through origin 'O' and cuts the axes of co-ordinates in points P and Q, then the equation of the locus of the foot of perpendicular from O to PQ is

•  (x²+y² )(1/x² +1/y² )=4a²
•  (x²+y² )² (1/x² +1/y²)=a²
•  (x²+y² )² (1/x² +1/y²)=4a²
•  (x²+y² )(1/x² +1/y² )=a²

Solution

Q8. The condition that the chord x cos⁡ a+ y sin⁡α-p=0 of x²+y²-a²=0 may subtend a right angle at the centre of the circle is

•  a²=2p²
•  p²=2a²
•  a=2p
•   p=2a

Solution

Q9.Six points (xi,yi ),i=1,2,…,6 are taken on the circle x²+y²=4 such that ∑_(i=1)⁶xi=8 and ∑_(i=1)⁶yi=4. The line segment joining orthocenter of a triangle made by any three points and the centroid of the triangle made by other three points passes through a fixed points (h,k), then h+k is

•  1
•  2
•  3
•  4

Solution

Q10.An equation for the line that passes through (10,-1) and is perpendicular to y=x²/4-2 is

•  4x+y=39
•  2x+y=19
•  x+y=9
•  x+2y=8