## Conic Section Quiz-19

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. If r1 and r2 are the radii of smallest and largest circles which passes through (5, 6) and touches the circle (x-2)2+y2=4, then r1 r2 is
•  4/41
•  41/4
•  5/41
•  41/6
Solution
Q2. The common chord of the circle x2+y2+6x+8y-7=0 and a circle passing through the origin, and touching the line y=x, always passes through the point
•  A(-1/2,1/2)
•  (1, 1)
•  (1/2, 1/2)
•  None of these
Solution
Q3. The distance from the centre of the circle x2+y2-2x to the common chord of the circles x2+y2+5x-8y+1=0 and x2+y2-3x+7y-25=0 is
•  2
•  4
•  34/13
•  26/17
Solution

Q4.   If two normals to a parabola y2=4ax intersect at right angles, then the chord joining their feet passes through a fixed point whose co-ordinates are
•  x(-2a,0)
•  (a,0)
•  (2a,0)
•  None of these
Solution
Q5. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is (axes are coordinate axes)
•  4/3
•  4/√3
•  2/√3
•  None of these
Solution
Q6. The point of intersection of the tangents at the point P on the ellipse x2a2 +y2b2 =1 and its corresponding point Q on the auxiliary circle meet on the line
•  x=a/e
•  x=0
•  y=0
•  None of these
Solution
Q7. If a line y=3x+1 cuts the parabola x2-4x-4y+20=0 at A and B, then the tangent of the angle subtended by line segment AB at origin is
•  (8√3)/205
•  (8√3)/209
•  -(8√3)/215
•  None of these
Solution
Q8. If C1:x2+y2=(3+2√2)2 be a circle and PA and PB are pair of tangents on C1, where P is any point on the director circle of C1, then the radius of smallest circle which touch C1 externally and also the two tangents PA and PB is
•  2√3-3
•  2√2-1
•  2√2-1
•  1
Solution
Q9.The equation of a line inclined at an angle Ï€/4 to the X-axis, such that the two circles x2+y2=4,x2+y2-10x-14y+65=0 intercept equal lengths on it, is
•  2x-2y-3=0
•  2x-2y+3=0
•  x-y+6=0
•  x-y-6=0
Solution
Q10.The number of possible tangents which can be drawn to the curve 4x2-9y2=36, which are perpendicular to the straight line 5x+2y-10=0 is
•  0
•  1
•  2
•  4

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Conic Section Quiz-19