## Conic Section Quiz-31

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 values of c such that the straight line y=4x+c touches the curve x^2/4+y^2/1=1 is
•   0
•   1
•   2
•   Infinite
Solution
Q2.  Let S be the focus of y^2=4x and a point P is moving on the curve such that its abscissa is increasing at the rate of 4 units/sec, then the rate of increase of projection of SP on x+y=1 when P is at (4,4) is
•  √2
•  -1
•  -√2
•  -3/√2
Q3.  The locus of the centre of a circle which cuts orthogonally the parabola y^2=4x at (1, 2) will pass though points
•   (3, 4)
•   (4, 3)
•   (5, 3)
•   (2, 4)
Solution

Q4.
The area of the triangle formed by the tangent and the normal to the parabola y^2=4ax, both drawn at the same end of the latus rectum, and the axis of the parabola is
•   2√2 a^2
•   2a^2
•   4a^2
•   None of these
Solution
Q5.  A square is inscribed in the circle x^2+y^2-2x+4y-93=0 with its sides parallel to the coordinate axis. The co-ordinates of its vertices are
•  (-6,-9),(-6,5),(8,-9),(8,5)
•  (-6,9),(-6,-5),(8,-9),(8,5)
•  (-6,-9),(-6,5),(8,9),(8,5)
•  (-6,-9),(-6,5),(8,-9),(8,- 5)
Solution
Q6.  A normal to the hyperbola x^2/4-y^2/1=1 has equal intercepts on positive x- and y-axes. If this normal touches the ellipse x^2/a^2 +y^2/b^2 =1, then a^2+b^2 is equal to
•   5
•   25
•   16
•   None of these
• Solution
Q7.  If the tangents are drawn from any point on the line x+y=3 to the circle x^2+y^2=9, then the chord of contact passes through the point
•   (3, 5)
•   (3, 3)
•  (5, 3)
•   None of these
Q8.  A straight line has its extremities on two fixed straight lines and cuts off from them a triangle of constant area c^2. Then the locus of the middle point of the line is
•  2xy=c^2
•  xy+c^2=0
•  4x^2 y^2=c
•  None of these
Solution
Q9. If the normals to the parabola y^2=4ax at three points P,Q and R meet at A and S be the focus, then SP.SQ.SR is equal to
•   a^2 SA
•   SA^3
•   aSA^2
•   None of these
Solution
Q10. If the line x cos⁡〖Î¸+y sin⁡〖Î¸=2〗 〗 is the equation of a transverse common tangent to the circles x^2+y^2=4 and x^2+y^2-6√3 x-6y+20=0, then the value of Î¸ is
•  5Ï€/6
•  2Ï€/3
•  Ï€/3
•  Ï€/6
Solution

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Conic Section Quiz-31