## Conic Section Quiz-15

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 number of common chords of the parabolas x=y2-6y+11 and y=x2-6x+1 are
•  1
•  2
•  4
•  6
Q2. Equation of the chord of contact of pair of tangents drawn to the ellipse 4x2+9y2=36 from the point (m,n) where m.n=m+n,m,nbeing non-zero positive integers is
•  2x+9y=18
•  2x+2y=1
•  4x+9y=18
•   None of these
Solution
Q3. ABCD is a square of unit area. A circle is tangent to two sides of ABCD and passes through exactly one of its vertices. The radius of the circle is
•   2-√2
•  √2-1
•  1/2
•  1/√2
Solution

Q4.   Let LL' be the latus rectum through the focus of the hyperbola x2/a2-y2/b2 =1 and A' be the farther vertex. If ∆A'LL' is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes)
•  √3
•  √3+1
•  (√3+1)/√2
•  (√3+1)/√3
Solution
Q5. The locus of the point of intersection of the lines √3x-y-4√3t=0 and √3tx+ty-4√3=0 (where t is a parameter) is a hyperbola whose eccentricity is
•  √3
•  2
•  2/√3
•  4/3
Solution
Q6. From any point on the hyperbola x2/a2 -y2/b2 =1 tangents are drawn to the hyperbola x2/a2 -y2/b2 =2. Then area cut-off by the chord of contact on the asymptotes is equal to
•  a/2
•  ab
•  2ab
•  4ab
Solution
Q7. If the angle between tangents drawn to x2 +y2 +2gx+2fy+c=0 form (0,0) is Ï€/2, then
•  g2+f2=3c
•  g2+f2=2c
•  g2+f2=5c
•  g2+f2=4c
Solution
Q8. The angle at which the circles (x-1)2+y2=10 and x^2+(y-2)2=5 intersect is
•  Ï€/6
•  Ï€/4
•  Ï€/3
•   Ï€/2
Solution
Q9.Angle between the tangents to the curve y=x2-5x+6 at the point (2, 0) and (3,0) is
•  Ï€/2
•  Ï€/3
•  Ï€/6
•  Ï€/4
Solution
Q10.The equation of the transverse and conjugate axes of a hyperbola are respectively x+2y-3=0,2x-y+4=0, and their respective lengths are √2 and 2/√3 . The equation of the hyperbola is
•  2/5 (x+2y-3)2-3/5 (2x-y+4)2=1
•  2/5 (2x-y+4)2-3/5 (x+2y-3)2=1
•  2(2x-y+4)2-3(x+2y-3)2=1
•  2(x+2y-3)2-3(2x-y+4)2=1

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