JEE Main 2021 — Circle Questions with Solutions

Two circles each of radius 5 units touch each other at the point ( 1 , 2 ) . If the equation of their common tangent is…

Let the tangent to the circle x 2 + y 2 = 25 at the point R ( 3 , 4 ) meet x -axis and y -axis at point P and Q , respe…

Two tangents are drawn from the point P - 1 , 1 to the circle x 2 + y 2 - 2 x - 6 y + 6 = 0 . If these tangents touch t…

Two tangents are drawn from a point P to the circle x 2 + y 2 - 2 x - 4 y + 4 = 0 , such that the angle between these t…

A circle C touches the line x = 2 y at the point 2 , 1 and intersects the circle C 1 : x 2 + y 2 + 2 y - 5 = 0 at two p…

If the variable line 3 x + 4 y = α lies between the two circles ( x - 1 ) 2 + ( y - 1 ) 2 = 1 and ( x - 9 ) 2 + (…

Let A 1 , 4 and B 1 , - 5 be two points. Let P be a point on the circle x - 1 2 + y - 1 2 = 1 , such that P A 2 + P B 2…

For the four circles M ,   N ,   O and P , following four equations are given: Circle M   :   x 2 +…

Let the lengths of intercepts on x -axis and y -axis made by the circle x 2 + y 2 + a x + 2 a y + c = 0 , a < 0 be…

Let the circle S : 36 x 2 + 36 y 2 - 108 x + 120 y + C = 0 be such that it neither intersects nor touches the co-ordina…