Circle questions
490 published questions with worked solutions.
- The angle between the pair of straight lines formed by joining the points of intersection of x^2+y^2=4 and y=3x+c to the origin...
- Consider the following statements: I. The lines 2x+3y+19=0 and 9x+6y-17=0 cut the coordinate axes in concyclic points II. The...
- The number of points on the line 3x+4y=5, which are at a distance of ^2 +2 cosec ^2 , R, from the point (1,3) is
- Let the equation of two diameters of a circle x^ 2 + y^ 2 - 2x + 2fy + 1 = 0 be 2px − y = 1 and 2x + py = 4p. Then the slope m...
- A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is
- Let a circle C touch the lines L_ 1 : 4x - 3y + K_ 1 = 0 and L_ 2 : 4x - 3y + K_ 2 = 0, K_ 1 , K_ 2 ℝ. If a line passing through...
- Let the abscissae of the two points P and Q be the roots of 2x^ 2 − rx + p = 0 and the ordinates of P and Q be the roots of x^ 2...
- Let the abscissae of the two points P and Q on a circle be the roots of x^ 2 - 4x - 6 = 0 and the ordinates of P and Q be the...
- If m is the slope of a common tangent to the curves x^ 2 /16 + y^ 2 /9 = 1 and x^ 2 + y^ 2 = 12, then 12m^ 2 is equal to :
- Let C be a circle passing through the points A(2, −1) and B(3, 4). The line segment AB is not a diameter of C. If r is the radius...
- Let B be the centre of the circle x^2+y^2-2x+4y+1=0. Let the tangents at two points P and Q on the circle intersect at the point...
- Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of k and 2...
- The circle passing through the point (−1, 0) and touching the y-axis at (0, 2) also passes through the point
- The straight line 2x − 3y = 1 divides the circular region x^2 + y^2 6 into two parts. If S = (2, 3 4 ), ( 5 2 , 3 4 ), ( 1 4 , -...
- The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x − 5y = 20 to the...
- Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 2 7 on y-axis is (are)
- A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 + y^2 = 16 and x^2 + y^2 = 1. Then
- The common tangents to the circle x^2 + y^2 = 2 and the parabola y^2 = 8x touch the circle at the points P, Q and the parabola at...
- For how many values of p, the circle x^2+y^2+2x+4y-p=0 and the coordinate axes have exactly three common points?
- A line y=mx+1 intersects the circle (x-3)^2+(y+2)^2=25 at the points P and Q. If the midpoint of the line segment PQ has...
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