## Conic Section Quiz-20

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. A circle passes through the points A(1,0),B(5,0) and touches the y-axis at C(0,h). If ∠ACB is maximum then
•  h=3√5
•   h=2√5
•  h=√5
•  h=2√10
Solution
Q2. The equation of the circle passing through the point of intersection of the circles x2+y2-4x-2y=8 and x2+y2-2x-4y=8 and the point (-1,4) is
•  x2+y2+4x+4y-8=0
•  x2+y2-3x+4y+8=0
•  x2+y2+x+y-8=0
•   x2+y2-3x-3y-8=0
Solution
Q3. The length of the latus rectum of the parabola whose focus is (u2/2g sin⁡2Î±,-u2/2g cos⁡2Î± ) and directrix is y=u2/2g is
•  u2/g cos2⁡Î±
•  u2/g cos⁡2Î±
•  (2u2)/g cos⁡2Î±
•  (2u2)/g cos2Î±
Solution

Q4.   If the line y-√3x+3=0 cuts the parabola y2=x+2 at P and Q, then AP∙AQ is equal to [where A≡(√(3,) 0)]
•  (2(√3+2))/3
•  (4√3)/2
•  (4(2-√(2)))/3
•  (4(√3+2))/3
Solution
Q5. If the tangents are drawn to the ellipse x2+2y2=2, then the locus of the mid point of the intercept made by the tangents between the coordinate axes is
•  1/(2x2 )+1/(4y2 )=1
•  1/(4x2 )+1/(2y2 )=1
•  x2/2+y2/4=1
•  x2/4+y2/2=1
Solution
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Q6. A circle with radius |a| and centre on y-axis slides along it and a variable lines through (a,0) cuts the circle at points P and Q. The region in which the point of intersection of tangents to the circle at point P and Q lies is represented by
•  y2≥4(ax-a2 )
•  y2≤4(ax-a2)
•  y≥4(ax-a2 )
•  y≤4(ax-a2)
Solution
Q7. The range of values of Î»(Î»>0) such that the angle Î¸ between the pair of tangents drawn from (Î»,0) to the circle x2+y2=4 lies in (Ï€/2,2Ï€/3) is
•  (4/√3,2√2)
•  ((0,√2)
•  (1, 2)
•  None of these
Solution
Q8. The eccentric angle of a point on the ellipse x2/4+y2/3=1 at a distance of 5/4 units from the focus on the positive x-axis, is
•  cos-1⁡(3/4)
•  Ï€-cos-1⁡⁡(3/4)
•  Ï€+ cos-1⁡⁡(3/4)
•  None of these
Solution
Q9.The number of common tangent (s) to the circles x2+y2+2x+8y-23=0 and x2+y2-4x-10y-19=0 is
•  1
•  2
•  3
•  4
Solution
Q10.If tangents PQ and PR are drawn from a point on the circle x2+y2=25 to the ellipse x2/4+y2/b2 =1,(b<4), so that the fourth vertex S of parallelogram PQSR lies on the circumcircle of triangle PQR, then eccentricity of the ellipse is
•  √5/4
•  √7/3
•  √7/4
•  4

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Conic Section Quiz-20