Circle questions
490 published questions with worked solutions.
- If the equation a|z|^2+ z+ z+d=0 represents a circle where a,d are real constants, then which of the following condition is...
- For the four circles M, N, O and P, following four equations are given : Circle M : x^2+y^2=1 Circle N : x^2+y^2-2x=0 Circle O :...
- Let r_1 and r_2 be the radii of the largest and smallest circles, respectively, which pass through the point (–4,1) and having...
- Let the circle S : 36x^2+36y^2-108x+120y+C=0 be such that it neither intersects nor touches the co-ordinate axes. If the point of...
- If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x-2)^2+(y-3)^2=25 at the...
- If one of the diameters of the circle x^2+y^2-2x-6y+6=0 is a chord of another circle 'C', whose center is at (2, 1), then its...
- The tangents are drawn from the point P(–1, 1) to the circle x^2+y^2-2x-6y+6=0. If these tangents touch the circle at points A...
- Let A = (x,y) R R|2x^2+2y^2-2x-2y=1 , B = (x,y) R R|4x^2+4y^2-16y-7=0 and C = (x,y) R R|x^2+y^2-4x-2y+5 r^2 . Then the minimum...
- Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept 6 5 on the x-axis. Then the radius of the circle...
- Let the equation x^2+y^2+px+(1-p)y+5=0 represent circles of varying radius r (0, 5). Then the number of elements in the set S = q...
- Let two circles of radius r_1 = 1 at centre (1, 1) and r_2 = 2 at centre (9, 1) with equation (x-9)^2+(y-1)^2=4. A common tangent...
- Let the lines (2-i)z=(2+i) z and (2+i)z+(i-2) z-4i=0, (here i^2=–1) be normal to a circle C. If the line iz + z+1+i = 0 is...
- The equation of a circle is Re(z^2)+2(Im(z))^2+2Re(z)=0, where z = x + iy. A line which passes through the center of the given...
- A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C_1: x^2+y^2+2y-5=0 at two points P and Q such...
- If a line along a chord of the circle 4x^2+4y^2+120x+675=0 passes through the point (–30, 0) and is tangent to the parabola...
- Let A(1, 4) and B(1, –5) be two points. Let P be a point on the circle (x-1)^2+(y-1)^2=1 such that (PA)^2+(PB)^2 have maximum...
- Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, –3) and...
- Let x^ 2 + y^ 2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x^ 2 at (2, 4). Then A + C is...
- Let a circle C : (x - h)^ 2 + (y - k)^ 2 = r^ 2 , k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle...
- The equation of the pair of straight lines parallel to x-axis and touching the circle x^2+y^2-6x-4y-12=0 is
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