Two circles and common tangents

JEE Main Mathematics · Circle · 8 questions, latest first

• Let the set of all values of r, for which the circles (x+1)^2+(y+4)^2=r^2 and x^2+y^2-4 x-2 y-4=0 intersect at two distinct…202622 January, Shift 1 · Q11
• Let C_1 be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C_2 be the circle with centre…20257 April, Shift 1 · Q12
• A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has…202522 January, Shift 1 · Q11
• Let the centre of a circle, passing through the points (0,0),(1,0) and touching the circle x^2+y^2=9, be (h, k). Then for all…20249 April, Shift 1 · Q29
• Let the circles C_1:(x-α)^2+(y-β)^2=r_1^2 and C_2:(x-8)^2+(y-15/2)^2=r_2^2 touch each other externally at the point (6,6). If the…20248 April, Shift 1 · Q15
• Let C: x^2+y^2=4 and C^′: x^2+y^2-4 λ x+9=0 be two circles. If the set of all values of λ so that the circles C and C^′ intersect…20241 February, Shift 1 · Q15
• If the circles (x+1)^2+(y+2)^2=r^2 and x^2+y^2-4 x-4 y+4=0 intersect at exactly two distinct points, then202430 January, Shift 1 · Q14
• The number of common tangents, to the circles x^2+y^2-18 x-15 y+131=0 and x^2+y^2-6 x-6 y-7=0, is202315 April, Shift 1 · Q13