Circles · JEE Main previous year questions

2018 6 questions

1. Q162018 · 16 Apr 2018 · Shift 1

   If a circle C, whose radius is 3, touches externally the circle, $x^2+y^2+2x-4y-4=0$ at the point (2, 2), then the length of the intercept cut by this circle C, on the x-axis is equal to :

   1. A.$2\sqrt{5}$
   2. B.$3\sqrt{2}$
   3. C.$\sqrt{5}$
   4. D.$2\sqrt{3}$
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   Answer: A

2. Q272018 · 16 Apr 2018 · Shift 1

   Let P be a point on the parabola, $x^2=4y$. If the distance of P from the center of the circle, $x^2+y^2+6x+8=0$ is minimum, then the equation of the tangent to the parabola at P, is :

   1. A.$x+4y-2=0$
   2. B.$x-y+3=0$
   3. C.$x+y+1=0$
   4. D.$x+2y=0$
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   Answer: C

3. Q242018 · 15 Apr 2018 · Shift 1

   A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, $y-4x+3=0$, then its radius is equal to :

   1. A.2
   2. B.$\sqrt{5}$
   3. C.$\sqrt{2}$
   4. D.1
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   Answer: A

4. Q222018 · 8 Apr 2018 · Shift 1

   Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :

   1. A.$\frac{3\sqrt{5}}{2}$
   2. B.$\sqrt{10}$
   3. C.$2\sqrt{10}$
   4. D.$3\sqrt{\frac{5}{2}}$
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   Answer: D

5. Q232018 · 8 Apr 2018 · Shift 1

   If the tangent at (1, 7) to the curve $x^2=y-6$ touches the circle $x^2+y^2+16x+12y+c=0$, then the value of c is :

   1. A.$95$
   2. B.$195$
   3. C.$185$
   4. D.$85$
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   Answer: A

6. Q252018 · 8 Apr 2018 · Shift 1

   Tangent and normal are drawn at P(16, 16) on the parabola $y^2=16x$, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and $\angle \mathrm{CPB}=\theta$, then a value of $\tan \theta$ is :

   1. A.$\frac{4}{3}$
   2. B.$\frac{1}{2}$
   3. C.$2$
   4. D.$3$
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   Answer: C