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

The set of all real values of for which exactly two common tangents can be drawn to the circles x^2+y^2-4 x-4 y+6=0 and x ^2+ y ^2-10 x -10 y + =0 is the interval:

Options

  1. A(12,32)
  2. B(18,42)
  3. C(12,24)
  4. D(18,48)

Correct answer

B. (18,42)

Step-by-step solution

The equations of the circles are x^2+y^2-10 x-10 y+ =0 and x^2+y^2-4 x-4 y+6=0 aligned &C₁= centre of (1)=(5,5) & C ₂= centre of (2)=(2,2) &d= distance between centres &= C ₁ C ₂= 9+9 = 18 &r₁= 50- , r₂= 2 & For exactly two common tangents we & have &r₁-r₂ 18 or < 42 & Required interval is (18,42) & aligned

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