Circle questions
490 published questions with worked solutions.
- A chord subtends an angle 120° at the centre of a unit circle. What is the length of the chord?
- What is the radius of the circle 4x^2+4y^2-20x+12y-15=0?
- Let G be a circle of radius R > 0. Let G_1, G_2, , G_n be n circles of equal radius r > 0. Suppose each of the n circles G_1,...
- Let C_1 be the circle of radius 1 with center at the origin. Let C_2 be the circle of radius r with center at the point A = (4,...
- If the circle x^ 2 + y^ 2 - 2gx + 6y - 19c = 0, g, c R passes through the point (6, 1) and its centre lies on the line x − 2cy =...
- The set of values of k, for which the circle C : 4x^ 2 + 4y^ 2 - 12x + 8y + k = 0 lies inside the fourth quadrant and the point...
- Let a circle C of radius 5 lie below the x-axis. The line L_ 1 : 4x + 3y + 2 = 0 passes through the centre P of the circle C and...
- Let dy/dx = (ax − by + a)/(bx + cy + a), where a, b, c are constants, represent a circle passing through the point (2, 5). Then...
- Let the tangents at two points A and B on the circle x^ 2 + y^ 2 - 4x + 3 = 0 meet at origin O(0, 0). Then the area of the...
- Let C be the centre of the circle x^ 2 + y^ 2 - x + 2y = 11/4 and P be a point on the circle. A line passes through the point C,...
- If one of the diameters of the circle x^ 2 + y^ 2 - 2 2x - 6 2y + 14 = 0 is a chord of the circle (x - 2 2 )^ 2 + (y - 2 2 )^ 2 =...
- Let the lines y + 2x = 11 + 7 7 and 2y + x = 2 11 + 6 7 be normal to a circle C : (x - h)^ 2 + (y - k)^ 2 = r^ 2 . If the line...
- Let AB be a chord of length 12 of the circle (x - 2)^ 2 + (y + 1)^ 2 = 169/4. If tangents drawn to the circle at points A and B...
- Let the mirror image of a circle c_ 1 : x^ 2 + y^ 2 - 2x - 6y + = 0 in line y = x + 1 be c_ 2 : 5x^ 2 + 5y^ 2 + 10gx + 10fy + 38...
- Let the tangent to the circle C_ 1 : x^ 2 + y^ 2 = 2 at the point M(−1, 1) intersect the circle C_ 2 : (x - 3)^ 2 + (y - 2)^ 2 =...
- A circle is drawn on the chord of a circle x^2+y^2=a^2 as diameter. The chord lies on the line x+y=a. What is the equation of the...
- The circle x^2+y^2+4x-7y+12=0, cuts an intercept on y-axis equal to
- Consider a circle C_1: x^2+y^2-4x-2y= -5. Let its mirror image in the line y = 2x + 1 be another circle C_2:...
- Let a common tangent to the curves y^2=4x and (x-4)^2+y^2=16 touch the curves at the points P and Q. Then (PQ)^2 is equal to...
- Two circles in the first quadrant of radii r_1 and r_2 touch the coordinate axes. Each of them cuts off an intercept of 2 units...
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