Circle Questions with Solutions

19 questions7 easy9 medium3 hard

In coordinate geometry, a circle is the set of points at a fixed distance (the radius) from a fixed point (the centre). This topic covers the standard equation (x - h)^2 + (y - k)^2 = r^2, the general equation x^2 + y^2 + 2gx + 2fy + c = 0 with centre (-g, -f), the diameter form, and parametric equations. Exam questions also test the position of a point relative to a circle, the condition for a line to be a tangent, equations of tangents and normals, the length of a tangent from an external point, and the intersection of two circles. The fastest approach is often to compare the distance from the centre to a line with the radius: equal means tangent, smaller means the line cuts the circle. Practise the circle questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
Segments of the lines $2 x + 3 y = 1$ and $4 x - 3 y = 11$ are diameters of a circle of area 153.94 square units. Then the equation of this circle with integer radius is:
A. $x^{2} + y^{2} + 4 x - 2 y - 44 = 0$ B. $x^{2} + y^{2} + 4 x - 2 y + 44 = 0$ C. $x^{2} + y^{2} - 4 x + 2 y - 44 = 0$ D. $x^{2} + y^{2} - 4 x + 2 y + 44 = 0$
easyAsked in NIMCET 2026View solution ›
Q2.
The equation $x^{2} + y^{2} + 4 x + 6 y + 13 = 0$ represents
A. a pair of coincident linesB. a pair of concurrent straight linesC. a parabolaD. a point circle
easyAsked in AMU MCA 2016View solution ›
Q3.
The radius of the circle passing through the foci of the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ and having its centre at (0, 3) is
A. 4 unitsB. 3 unitsC. $12$ unitsD. $\frac{7}{2}$ units
easyAsked in NIMCET 2015View solution ›
Q4.
The point of intersection of the circle $x^{2} + y^{2} + 10 x - 12 y + 51 = 0$ and the line $x + 3 y = 3$ is
A. $(- 6, 3)$ B. $(3, - 6)$ C. $(6, - 3)$ D. $(- 3, 6)$
easyAsked in NIMCET 2018View solution ›
Q5.
The equation of the circle passing through the point (4, 6) and whose diameters are along $x + 2 y - 5 = 0$ and $3 x - y - 1 = 0$ is
A. $x^{2} + y^{2} - 2 x - 6 y - 20 = 0$ B. $x^{2} + y^{2} - 6 x - 2 y - 20 = 0$ C. $x^{2} + y^{2} - 2 x - 4 y - 20 = 0$ D. $x^{2} + y^{2} - 4 x - 2 y - 20 = 0$
easyAsked in NIMCET 2019View solution ›
Q6.
For the two circles $x^{2} + y^{2} = 16$ and $x^{2} + y^{2} - 2 y = 0$ , there is/are
A. One pair of common tangentsB. Two pairs of common tangentsC. Three pairs of common tangentsD. No common tangents
easyAsked in NIMCET 2019View solution ›
Q7.
A circle with its center in the first quadrant touches both the coordinate axes and the line $x - y - 2 = 0$ . Then the area of the circle is
A. $\frac{π}{2}$ B. $4 π$ C. $π$ D. $2 π$
easyAsked in NIMCET 2025View solution ›