Circle questions
490 published questions with worked solutions.
- The common tangent to the circles x^2 + y^2 = 4 and x^2 + y^2 + 6x + 8y - 24 = 0 also passes through the point:
- The area (in sq. units) of the smaller of the two circles that touch the parabola, y^2 = 4x at the point (1, 2) and the x-axis is:
- If the circles x^2 + y^2 + 5Kx + 2y + K = 0 and 2(x^2 + y^2) + 2Kx + 3y - 1 = 0, (K ∈ R), intersect at the points P and Q, then...
- The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, −3), then its radius is:
- If the circles x^2 + y^2 - 16x - 20y + 164 = r^2 and (x - 4)^2 + (y - 7)^2 = 36 intersect at two distinct points, then:
- If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90°, then the length (in cm)...
- Let C_1 and C_2 be the centres of the circles x^2 + y^2 - 2x - 2y - 2 = 0 and x^2 + y^2 - 6x - 6y + 14 = 0 respectively. If P and...
- A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the...
- The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of...
- A square is inscribed in the circle x^2 + y^2 - 6x + 8y - 103 = 0 with its sides parallel to the coordinate axes. Then the...
- Two circles with equal radii are intersecting at the points (0, 1) and (0, −1). The tangent at the point (0, 1) to one of the...
- If the area of an equilateral triangle inscribed in the circle x^2 + y^2 + 10x + 12y + c = 0 is 27 3 sq units then c is equal to:
- If a circle C passing through the point (4, 0) touches the circle x^2 + y^2 + 4x - 6y = 12 externally at the point (1, −1), then...
- A circle touching the x-axis at (3, 0) and making an intercept of length 8 on the y-axis passes through the point:
- Let the tangents drawn from the origin to the circle, x^2+y^2-8x-4y+16=0 touch it at the points A and B. The (AB)^2 is equal to:
- If the curves, x^2-6x+y^2+8=0 and x^2-8y+y^2+16-k=0, (k > 0) touch each other at a point, then the largest value of k is...
- A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a...
- Let the locus of the midpoints of the chords of the circle x² + (y − 1)² = 1 drawn from the origin intersect the line x + y = 1...
- Let C : x² + y² = 4 and C′ : x² + y² − 4λx + 9 = 0 be two circles. If the set of all values of λ so that the circles C and C′...
- Let C be a circle with radius 10 units and centre at the origin. Let the line x + y = 2 intersects the circle C at the points P...
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