Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2014MathematicsCircleActual

For the two circles x^2+y^2=16 and x^2+y^2-2 y=0 , there is/are

Options

  1. Aone pair of common tangents
  2. Btwo pair of common tangents
  3. Cthree pair of common tangents
  4. Dno common tangent

Correct answer

D. no common tangent

Step-by-step solution

Let, x^2+y^2=16 or x^2+y^2=4^2 radius of circle r₁=4 , centre C ₁(0,0) we have, x^2+y^2-2 y=0 aligned & x^2+ (y^2-2 y+1 )-1=0 or x^2+(y-1)^2 =& 1^2 aligned Radius 1, centre C ₂(0,1) aligned & |C₁ C₂ |=1 & |r₂-r₁ |=|4-1|=3 & |C₁ C₂ | < |r₂-r₁ | aligned no common tangents for these two circles.

Practice Circle on Quantrex Academy →

More from Circle

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The circle with centre (1, 2) and touching the straight line 3x + 4y = 2026Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from th 2026Let C be a circle having centre in the first quadrant and touching the x -axis at a distance of 3 units from the origin. If the circle C has an intercept of length 6 3 on y -axis, 2026Let the line x - y = 4 intersect the circle C: (x-4)^2 + (y+3)^2 = 9 at the points Q and R . If P( , ) is a point on C such that PQ = PR , then (6 + 8 )^2 is equal to __________. 2026Let the centre of the circle x^2 + y^2 + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x - y = 4 . Let the area of an equilateral triangle inscribed in the circl 2026Let P be a moving point on the circle x^2 + y^2 - 6x - 8y + 21 = 0 . Then, the maximum distance of P from the vertex of the parabola x^2 + 6x + y + 13 = 0 is equal to: 2026Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0 are bisected by the y -axis. If the other ends of these chords are R and S , and the mid p 2026Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k-1)y + 3 = 0 and 2x + k^2 y - 4 = 0 . If the line x - y + 2026 Full Circle list All JEE Main PYQs