JEE Main 2024 — Circle Questions with Solutions

Four distinct points ( 2 k , 3 k ) , ( 1 , 0 ) , ( 0 , 1 ) and ( 0 , 0 ) lie on a circle for k equal to :

Let a circle passing through (2,0) have its centre at the point (h, k). Let (xc, yc ) be the point of intersection of t…

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 cir…

Consider two circles C 1 : x 2 + y 2 = 25 and C 2 : ( x - α ) 2 + y 2 = 16 , where α ∈ ( 5 , 9 ) . Let the angle betwee…

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 poin…

Let the circles C₁:(x-α)²+(y-β)²=r₁² and C₂:(x-8)²+ (y-(15)/(2) )²=r₂² touch each other externally at the point (6,6).…

If one of the diameters of the circle x 2 + y 2 - 10 x + 4 y + 13 = 0 is a chord of another circle C , whose center is…

Consider a circle x - α 2 + y - β 2 = 50 , where α , β > 0 . If the circle touches the line y + x = 0 at the point P ,…

Let A B C D and A E F G be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the p…

Let the locus of the mid points of the chords of circle x 2 + y − 1 2 = 1 drawn from the origin intersect the line x +…