Circle questions
490 published questions with worked solutions.
- Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal...
- Suppose that two chords, drawn from the point (1, 2) on the circle x² + y² + x − 3y = 0 are bisected by the y-axis. If the other...
- Let C be a circle having centre in the first quadrant and touching the x-axis at a distance of 3 units from the origin. If the...
- Let the line x−y=4 intersect the circle C : (x−4)²+(y+3)²=9 at the points Q and R. If P(α,β) is a point on C such that PQ=PR,...
- Let the centre of the circle x²+y²+2gx+2fy+25=0 be in the first quadrant and lie on the line 2x−y=4. Let the area of an...
- Consider the circle C : x² + y² − 6x − 8y − 11 = 0. Let a variable chord AB of the circle C subtend a right angle at the origin....
- Let a circle passing through (2, 0) have its centre at the point (h, k). Let (x_c, y_c) be the point of intersection of the lines...
- Let the centre of a circle, passing through the point (0, 0), (1, 0) and touching the circle x² + y² = 9, be (h, k). Then for all...
- 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, whose...
- Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for k equal to :
- Equations of two diameters of a circle are 2x – 3y = 5 and 3x – 4y = 7. The line joining the points (–22/7, –4) and (–1/7, 3)...
- Consider two circles C₁ : x² + y² = 25 and C₂ : (x − α)² + y² = 16, where α ∈ (5, 9). Let the angle between the two radii (one to...
- If one of the diameters of the circle x² + y² – 10x + 4y + 13 = 0 is a chord of another circle C, whose center is the point of...
- Let the lengths of intercepts on x-axis and y-axis made by the circle x^2+y^2+ax+2ay+c=0, (a < 0) be 2 2 and 2 5, respectively....
- The locus of the midpoints of the chord of the circle, x^2+y^2=25 which is tangent to the hyperbola, x^2 9 - y^2 16 =1 is :
- Let ABCD be a square of side of unit length. Let a circle C_1 centered at A with unit radius is drawn. Another circle C_2 which...
- 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, respectively. If r is the...
- The line 2x – y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x – 2y = 4. Then the...
- Choose the incorrect statement about the two circles whose equations are given below : x^2+y^2-10x-10y+41=0 and...
- Choose the correct statement about two circles whose equations are given below : x^2+y^2-10x-10y+41=0 and x^2+y^2-22x-10y+137=0
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