## Conic Section Quiz-37

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 the distance between two parallel tangents drawn to the hyperbola x^2/9-y^2/49=1 is 2, then their slope is equal to
•   ±5/2
•   ±4/5
•   ±7/2
•   None of these
Solution
Q2.  If y_1,y_2 and y_3 are the ordinates of the vertices of a triangle inscribed in the parabola y^2=4ax, then its area is
•  1/2a (y_1-y_2 )(y_2-y_3 )(y_3-y_1 )
•  1/4a (y_1-y_2 )(y_2-y_3 )(y_3-y_1 )
•  1/8a (y_1-y_2 )(y_2-y_3 )(y_3-y_1 )
•  None of these
Q3.  The chord of contact of tangents from three points A,B,C to the circle x^2+y^2=a^2 are concurrent, then A,B,C will
•   Be concylic
•   Be collinear
•   Form the vertices of a triangle
•   None of these
Solution

Q4.
If the eccentricity of the ellipse x^2/(a^2+1)+y^2/(a^2+2)=1 is 1/√6, then latus rectum of ellipse is
•   5/√6
•   10/√6
•   8/√6
•   None of these
Solution
Q5.  Let a and b represent the length of a right triangle’s legs. If d is the diameter of a circle inscribed into the triangle, and D is the diameter of a circle circumscribed on the triangle, then d+D equals
•  a+b
•  2(a+b)
•  1/2(a+b)
•  √(a^2+b^2 )
Solution
Q6.  A water jet from a fountain reaches its maximum height of 4 m at a distance 0.5 m from the vertical passing through the point O of water outlet. The height of the jet above the horizontal OX at a distance of 0.75 m from the point O is
•   5 m
•   6 m
•   3 m
•   7 m
• Solution
Q7.  The equation of the transverse axis of the hyperbola (x-3)^2+(y+1)^2=(4x+3y)^2 is
•   x+3y=0
•   4x+3y=9
•  3x-4y=13
•   4x+3y=0
Q8.  The eccentricity of the conjugate hyperbola of the hyperbola x^2-3y^2=1 is
•  2
•  2/√3
•  4
•  4/5
Solution
Q9. Two congruent circles with centres at (2, 3) and (5, 6), which intersect at right angles, have radius equal to
•   2√2
•   3
•   4
•   None
Solution
Q10. If y=mx+c touches the parabola y^2=4a(x+a), then
•  c=a/m
•  c=am+a/m
•  c=a+a/m
•  None of these
Solution

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Conic Section Quiz-37