Circle questions
490 published questions with worked solutions.
- Let a and b be any two numbers satisfying 1 a^2 + 1 b^2 = 14. Then, the foot of perpendicular from the origin on the variable...
- If the point (1, 4) lies inside the circle x^2 + y^2 - 6x + 10y + p = 0 and the circle does not touch or intersect the coordinate...
- The set of all real values of λ for which exactly two common tangents can be drawn to the circles x^2 + y^2 - 4x - 4y + 6 = 0 and...
- Let L_1 be the length of the common chord of the curves x^2 + y^2 = 9 and y^2 = 8x, and L_2 be the length of the latus rectum of...
- For the two circles x^2 + y^2 = 16 and x^2 + y^2 - 2y = 0, there is/are
- The equation of the circle described on the chord 3x + y + 5 = 0 of the circle x^2 + y^2 = 16 as the diameter is
- If P, P′ represent the complex number z_1 and its additive inverse respectively then the complex equation of the circle with PP′...
- If the chord y=mx+1 of the circle x^2+y^2=1 subtends an angle of measure 45^ at the major segment of the circle then the value of...
- If the equation of a circle is ax^2 + (2a-3)y^2 - 4x - 1 = 0 then its centre is
- If 2x^2 + xy + 2y^2 + ( - 4)x + 6y - 5 = 0 is the equation of a circle then its radius is
- The equation x^2 + y^2 - 2x + 4y + 5 = 0 represents
- The number of integral values of for which x^2 + y^2 + x + (1- )y + 5 = 0 is the equation of a circle whose radius cannot exceed...
- If 2(x^2 + y^2) + 4 x + ^2 = 0 represents a circle of meaningful radius then the range of real values of is
- The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines x^2 - y^2 - 2x + 4y...
- Two vertices of an equilateral triangle are (-1, 0) and (1, 0), and its third vertex lies above the x-axis. The equation of the...
- A triangle is formed by the lines whose combined equation is given by (x + y - 4)(xy - 2x - y + 2) = 0. The equation of its...
- If the centroid of an equilateral triangle is (1, 1) and its one vertex is (-1, 2) then the equation of its circumcircle is
- The equation of the circle whose one diameter is PQ, where the ordinates of P, Q are the roots of the equation x^2 + 2x - 3 = 0...
- A circle touches the y-axis at (0, 2) and has an intercept of 4 units on the positive side of the x-axis. Then the equation of...
- C_1 is a circle of radius 1 touching the x-axis and the y-axis. C_2 is another circle of radius > 1 and touching the axes as well...
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