Conic Section Quiz-14

Conic Section Quiz-14

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. The exhaustive set of values of α^2 such that there exists a tangent to the ellipse x²+α² y²=α² such that the portion of the tangent intercepted by the hyperbola α² x²-y²=1 subtends a right angle at the centre of the curves is

•  [(√5+1)/2, 2]
•  (1, 2]
•  [(√5-1)/2, 1)
•  [(√5-1)/2, 1) ∪ (1,(√5+1)/2]

Q2. If P(x1,y1 ),Q(x2,y2 ),R(x3,y3 ) and S(x4,y4) are four con-cyclic points on the rectangular hyperbola xy=c²2, then coordinates of the orthocentre of the triangle PQR is

•  (x4,-y4)
•  (x_4,y_4)
•  (-x4,-y4)
•  (-x4,y4)

Solution

Q3. Angle subtended by common tangents of two ellipses 4(x-4)²+25y²=100 and 4(x+1)²=4 at origin is

•  π/3
•  π/4
•  π/6
•  π/2

Solution

Q4.   From a point (sin⁡θ,cos⁡θ) if three normals can be drawn to the parabola y²=4ax then the value of ‘a’ is

•  (1/2,1)
•  (1/2 0)
•  [1/2,1]
•  (-1/2,0)∪(0,1/2)

Solution

Q5. The tangent at a point P on the hyperbola x²/a² -y²/b² =1 meets one of the directrix in F. If PF subtends an angle θ at the corresponding focus, then θ equals

•  π/4
•  π/2
•  3π/4
•  π

Solution

Q6. Let y=f(x) be a parabola, having its axis parallel to y–axis, which is touched by the line y=x at x=1, then

•  2f(0)=1-f'(0)
•  f(0)+f'(0)+f''(0)=1
•  f'(1)=1
•  f'(0)=f'(1)

Solution

Q7. The curve described parametrically by x=t²+ t+1,y=t²-t+1 represents

•  A pair of straight lines
•  An ellipse
•  A parabola
•  A hyperbola

Solution

Q8. Locus of the feet of the perpendiculars drawn from either focus on a variable tangent to the hyperbola 16y²-9x²=1 is

•  x²+y²=9
•  x²+y²=1/9
•  x²+y²=7/144
•   x²+y²=1/16

Solution

Q9.A line of fixed length a+b moves so that its ends are alwayes on two fixed perpendicular straight lines, then the locus of a point, which divides this line into portions of lenghts a and b is a/an

•  Ellipse
•  Parabola
•  Straight line
•  None of these

Solution

Q10.A variable chord of the hyperbola x²/a² -y²/b² =1 (b>a) subtends a right angle at the centre of the hyperbola, if this chord touches

•  A fixed circle concentric with the hyperbola
•  A fixed ellipse concentric with the hyperbola
•  A fixed hyperbola concentric with the hyperbola
•  A fixed parabola having vertex at (0, 0)