Circle questions
490 published questions with worked solutions.
- If the circles x^2 + y^2 - 2x = 0 and x^2 + y^2 + 2 y = 4 have only one common tangent then is
- A square is inscribed in the circle x^2 + y^2 - 2x - 4y = 0 whose sides are parallel to the axes of reference. A vertex of the...
- If the two circles (x-1)^2+(y-3)^2=r^2 and x^2+y^2-8x+2y+8=0 intersect in two distinct points then
- P and Q are two points on the curve x^2 + y^2 = a^2, where POQ = 2 , O being the origin. The equation of the tangent to the curve...
- The tangent to the curve y=x^2+6 at (1,7) touches the circle x^2+y^2+16x+12y+c=0 at the point
- If the circle passing through the points (0,0), (1,0) and (0,1) also passes through the point ( , 1 ) then is
- ABCD is a quadrilateral in which a circle is inscribed. STATEMENT-1: The lengths of the sides of the quadrilateral can be in AP....
- If A = (x, y) x^2 + y^2 4 and B = (x, y) (x-3)^2 + y^2 4 and the point P (a, a - 12 ) belongs to the set B - A then the set of...
- C_1, C_2, C_3, is a sequence of circles such that C_ n+1 is the director circle of C_n. If the radius of C_1 is a then the area...
- The centre of a circle which touches the line 2x - y = 1 at (1, 1) and also touches the line 2x + y = 4 is
- Four vertices of a square are ( 3, 3). If (a, a) is a point inside the square but falls outside the circle x^2 + y^2 = 1 then the...
- The equation of a diameter of a circle passing through the origin is x + y = 1 and the greatest distance of any point of the...
- If the point (a, a + 1) belongs to the interior of the region bounded by the curve y = 5 - x^2 and the x-axis then a belongs to
- The intercept on the line y = x by the circle x^2 + y^2 - 2x = 0 is AB. The equation of the circle on AB as a diameter is
- Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on...
- If the tangent at the point P on the circle x^2 + y^2 + 6x + 6y = 2 meets the straight line 5x - 2y + 6 = 0 at a point Q on the...
- Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169. STATEMENT-1: The tangents are mutually perpendicular....
- Match the statement in **Column I** with the properties in **Column II**. Column I: (A) Two intersecting circles (B) Two mutually...
- Consider L_1 : 2x + 3y + p - 3 = 0, L_2 : 2x + 3y + p + 3 = 0, where p is a real number and C : x^2 + y^2 + 6x - 10y + 30 = 0....
- Tangents drawn from the point P(1, 8) to the circle x^2 + y^2 - 6x - 4y - 11 = 0 touch the circle at the points A and B. The...
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