Circle questions
490 published questions with worked solutions.
- The intercept on the line y = x by the circle x^2 + y^2 - 2x = 0 is AB. The equation of the circle with AB as a diameter is
- Two circles, each of radius 5, have a common tangent at (1, 1) whose equation is 3x + 4y - 7 = 0. Then their centres are
- The equation of the circumcircle of the regular hexagon whose two consecutive vertices have the coordinates (-1, 0) and (1, 0)...
- If p and q be the longest distance and the shortest distance respectively of the point (-7, 2) from any point ( , ) on the curve...
- The equation of the circumcircle of an equilateral triangle is x^2 + y^2 + 2gx + 2fy + c = 0 and one vertex of the triangle is...
- Let f(x, y) = 0 be the equation of a circle. If f(0, ) = 0 has equal roots = 2, 2, and f( , 0) = 0 has roots = 45, 5 then the...
- The length of the chord of the circle x^2 + y^2 + 4x - 7y + 12 = 0 along the y-axis is
- If the line y - 1 = m(x - 1) cuts the circle x^2 + y^2 = 4 at two real points then the number of possible values of m is
- The length of the chord of the circle x^2 + y^2 = 9 passing through (3, 0) and perpendicular to the line y + x = 0 is
- The number of points on the circle 2x^2 + 2y^2 - 3x = 0 which are at a distance 2 from the point (-2, 1) is
- The equation of the diameter of the circle 3(x^2 + y^2) - 2x + 6y - 9 = 0 which is perpendicular to the line 2x + 3y = 12 is
- The equation of a circle C is x^2 + y^2 - 6x - 8y - 11 = 0. The number of real points at which the circle drawn with the points...
- The equation of the circle of radius 2 2 whose centre lies on the line x - y = 0 and which touches the line x + y = 4, and whose...
- The equation of the chord of the circle x^2 + y^2 = 25 of length 8 that passes through the point (2 3, 2) and makes an acute...
- The number of points with integral coordinates that are interior to the circle x^2 + y^2 = 16 is
- The range of values of a for which the point (a, 4) is outside the circles x^2 + y^2 + 10x = 0 and x^2 + y^2 - 12x + 20 = 0 is
- A region in the x-y plane is bounded by the curve y = 25 - x^2 and the line y = 0. If the point (a, a + 1) lies in the interior...
- If (2, 4) is a point interior to the circle x^2 + y^2 - 6x - 10y + = 0 and the circle does not cut the axes at any point then...
- The range of values of [0, 2 ] for which (1 + , ) is an interior point of the circle x^2 + y^2 = 1 is
- The range of values of r for which the point (-5 + r 2 , -3 + r 2 ) is an interior point of the major segment of the circle x^2 +...
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