Circle questions
490 published questions with worked solutions.
- A square is inscribed in the circle x² + y² − 10x − 6y + 30 = 0. One side of this square is parallel to y = x + 3. If (x_i, y_i)...
- Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3, 2) and parallel to the...
- Let the line 2x + 3y − k = 0, k > 0, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the...
- Let the circle C_1: x² + y² − 2(x + y) + 1 = 0 and C_2 be a circle having centre at (−1, 0) and radius 2. If the line of the...
- Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the...
- If a line, y = mx + c is a tangent to the circle, (x-3)^2+y^2=1 and it is perpendicular to a line L_1, where L_1 is the tangent...
- The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x^2+y^2-2x-4y+4=0 at two distinct...
- The diameter of the circle, whose centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3...
- 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...
- The circle passing through the intersection of the circles, x^2+y^2-6x=0 and x^2+y^2-4y=0, having its centre on the line. 2x – 3y...
- Let PQ be a diameter of the circle x^2+y^2=9. If and are the lengths of the perpendiculars from P and Q on the straight line, x +...
- If the length of the chord of the circle, x^2+y^2=r^2 (r > 0) along the line, y – 2x = 3 is r, then r^2 is equal to :
- The equation z z+a z+ az+b=0, b R represents a circle, if
- If z is a complex number in the Argand plane, then the equation |z-2|^2+|z+2|^2=8 represents
- The equation z= a+ r^2 z-a , r>0 represents
- The centre and the radius of the circle z z+(2+3i) z+(2-3i)z+12=0 are respectively
- The equation z z+(2-3i)z+(2+3i) z+4=0 represents a circle of radius
- The equation of a circle whose radius and centre are r and z_0 respectively, is
- The equation z z+(4-3i)z+(4+3i) z+5=0 represents a circle of radius
- Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k − 1)y...
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