Circle questions
490 published questions with worked solutions.
- The circle passing through (1, –2) and touching the axis of x at (3,0) also passes through the point -
- The equation of the circle passing through the foci of the ellipse x^2 16 + y^2 9 =1, and having centre at (0, 3) is -
- If P is a point on the circle x^2 + y^2 = 4, Q is a point on the straight line 5x + y + 2 = 0 and x - y + 1 = 0 is the...
- Let the set of all values of r, for which the circles (x+1)^2+(y+4)^2=r^2 and x^2+y^2-4x-2y-4=0 intersect at two distinct points...
- Let a circle of radius 4 pass through the origin O, the points A(- 3 a, 0) and B(0, - 2 b), where a and b are real parameters and...
- Let y = x be the equation of a chord of the circle C_1 (in the closed half-plane x 0) of diameter 10 passing through the origin....
- Let the circle x^2+y^2=4 intersect x-axis at the points A(a,0), a>0 and B(b,0). Let P(2 , 2 ), 0< < 2 and Q(2 ,2 ) be two points...
- Let the circle C touch the line x – y + 1 = 0, have the centre on the positive x-axis, and cut off a chord of length 4 13 along...
- Let the line x + y = 1 meet the circle x^2 + y^2 = 4 at the points A and B. If the line perpendicular to AB and passing through...
- If the four distinct points (4, 6), (–1, 5), (0, 0) and (k, 3k) lie on a circle of radius r, then 10k + r^2 is equal to
- Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and...
- If one of the diameters of the circle, given by the equation, x^2 + y^2 - 4x + 6y - 12 = 0, is a chord of a circle S, whose...
- The radius of a circle, having minimum area, which touches the curve y = 4 - x^2 and the lines, y = |x| is :
- If a circle C, whose radius is 3, touches externally the circle, x^2 + y^2 + 2x - 4y - 4 = 0 at the point (2, 2), then the length...
- The sum of the squares of the lengths of the chords intercepted on the circle, x^2 + y^2 = 16, by the lines, x + y = n, n ∈ N,...
- The tangent and the normal lines at the point ( 3, 1) to the circle x^2 + y^2 = 4 and the x-axis form a triangle. The area of...
- If a tangent to the circle x^2 + y^2 = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the...
- If the line ax + y = c, touches both the curves x^2 + y^2 = 1 and y^2 = 4 2 ,x, then |c| is equal to:
- A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y - 4x + 3 = 0, then its radius is equal to
- The tangent to the circle C_1 : x^2 + y^2 - 2x - 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C_2 whose...
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