## Conic Section Quiz-18

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. An equilateral triangle SAB is inscribed in the parabola y2=4ax having its focus at ‘S'. If chord AB lies towards the left of S, then side length of this triangel is
•  2a(2-√3)
•  4a(2-√3)
•   a(2-√3)
•  8a(2-√3)
Solution
Q2. If Î±-Î²= constant, then the locus of the point of intersection of tangents at P(a cos⁡Î±,bsin⁡Î± ) and Q(a cos⁡Î²,b sin⁡Î² ) to the ellipse x2/a2 +y2/b2 =1 is
•  A circle
•  A straight line
•  An ellipse
•  A parabola
Solution
Q3. A straight line I_1 with equation x-2y+10=0 meets the circle with equation x2+y2=100 at B in the first quadrant. A line through B, perpendicular to l1 cuts y-axis at P(0,t). The value of ‘t’ is
•  12
•  15
•  20
•  25
Solution

Q4.   If the equation of any two diagonals of a regular pentagon belongs to family of lines (1+2Î»)y-(2+Î»)x+1-Î»=0 and their lengths are sin⁡36°, then locus of centre of circle circumscribing the given pentagon (the triangles formed by these diagonals with sides of pentagon have no side common) is
•  x2+y2-2x-2y+1+sin272°=0
•  x2+y2-2x-2y+cos2⁡72°=0
•  x2+y2-2x-2y+1+cos272°=0
•  x2+y2-2x-2y+sin272°=0
Solution
Q5. If the line x-1=0 is the directrix of the parabola y2-kx+8=0, then one of the values of k is
•  1/8
•  8
•  4
•  1/4
Solution
Q6. The length of the major axis of the ellipse (5x-10)2+(5y+15)2=(3x-4y+7)2/4 is
•  10
•  20/3
•  20/7
•  4
Solution
Q7. If the circumference of the circle x2+y2+8x+8y-b=0 is bisected by the circle x2+y2-2x+4y+a=0, then a+b equals to
•  50
•  56
•  -56
•  -34
Solution
Q8. The line x-y=1 intersects the parabola y2=4x at A and B. Normals at A and B intersect at C. If D is the point at which line CD is normal to the parabola, then coordinates of D are
•  (4,-4)
•  (4, 4)
•  (-4,-4)
•  None of these
Solution
Q9.The locus of a point which moves such that the sum of the squares of its distance from three vertices of a triangle is constant is a/an
•  Circle
•  Straight line
•  Ellipse
•  None of these
Solution
Q10.A circle with centre (a,b) passes through the origin. The equation of the tangent to the circle at the origin is
•  ax-by=0
•  ax+by=0
•  bx-ay=0
•  bx+ay=0

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Conic Section Quiz-18