Circle questions
490 published questions with worked solutions.
- Lines are drawn through the point P(−2, −3) to meet the circle x^2 + y^2 - 2x - 10y + 1 = 0. The length of the line segment PA, A...
- The equations of two circles are x^2 + y^2 + 2 x + 5 = 0 and x^2 + y^2 + 2 y + 5 = 0. P is any point on the line x - y = 0. If PA...
- The common chord of the circle x^2 + y^2 + 6x + 8y - 7 = 0 and a circle passing through the origin, and touching the line y = x,...
- A tangent to the circle x^2 + y^2 = 1 through the point (0, 5) cuts the circle x^2 + y^2 = 4 at A and B. The tangents to the...
- If the common chord of the circles x^2 + (y - )^2 = 16 and x^2 + y^2 = 16 subtend a right angle at the origin then is equal to
- The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x^2 + y^2 = 9 is
- The equation of a circle is x^2 + y^2 = 4. The centre of the smallest circle touching this circle and the line x + y = 5 2 has...
- The members of a family of circles are given by the equation 2(x^2 + y^2) + x - (1 + ^2)y - 10 = 0. The number of circles...
- The equation of the circle with the chord y=2x of the circle x^2+y^2-10x=0 as its diameter is
- A circle of radius 2 touches the coordinate axes in the first quadrant. If the circle makes a complete rotation on the x-axis...
- The angle between a pair of tangents drawn from a point P to the curve x^2+y^2+4x-6y+9 ^2 +13 ^2 =0 is 2 . The locus of P is
- The locus of the middle points of chords of length 4 of the circle x^2+y^2=16 is
- The locus of the centres of circles passing through the origin and intersecting the fixed circle x^2+y^2-5x+3y-1=0 orthogonally is
- The equation of a circle C_1 is x^2+y^2-4x-2y-11=0. A circle C_2 of radius 1 rolls on the outside of the circle C_1. The locus of...
- Circles are drawn through the point (3,0) to cut an intercept of length 6 units on the negative direction of the x-axis. The...
- The locus of a point from which the lengths of the tangents to the circles x^2+y^2=4 and 2(x^2+y^2)-10x+3y-2=0 are equal is
- The locus of the centres of the circles passing through the intersection of the circles x^2+y^2=1 and x^2+y^2-2x+y=0 is
- P( 2, 2) is a point on the circle x^2+y^2=4 and Q is another point on the circle such that arc PQ= 14 circumference. The...
- Circles x^2+y^2=1 and x^2+y^2-8x+11=0 cut off equal intercepts on a line through the point (-2, 12 ). The slope of the line is
- Let L_1 be a straight line passing through the origin and L_2 be the straight line x+y=1. If the intercepts made by the circle...
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