List of top Mathematics Questions on circle asked in MET

The equation of mirror image of the circle \(x^2 + y^2 - 6x - 10y + 33 = 0\) about the line \(y = x\) is:
If 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 is a right angle, then \(c^2\) is:
Equation of tangent to the circle \(x^2 + y^2 - 2x - 2y + 1 = 0\) perpendicular to \(y = x\) is given by
The locus of centre of circles which cut orthogonally the circle \(x^2 + y^2 - 4x + 8 = 0\) and touches \(x + 1 = 0\), is
The radical centre of the system of circles, \[ x^2 + y^2 + 4x + 7 = 0,\quad 2(x^2 + y^2) + 3x + 5y + 9 = 0 \] and \(x^2 + y^2 + y = 0\) is
The point on the straight line \(y = 2x + 11\) which is nearest to the circle \(16(x^2 + y^2) + 32x - 8y - 50 = 0\), is
The number of common tangents to two circles \(x^2 + y^2 = 4\) and \(x^2 + y^2 - 8x + 12 = 0\) is:
The equation of circle which passes through the origin and cuts off intercepts 5 and 6 from the positive parts of the axes respectively, is \( \left(x - \frac{5}{2}\right)^2 + (y - 3)^2 = \lambda \), where \( \lambda \) is
A rhombus is inscribed in the region common to the two circles \( x^2 + y^2 - 4x - 12 = 0 \) and \( x^2 - y^2 + 4x - 12 = 0 \) with two of its vertices on the line joining the centres of the circles. The area of rhombus is
A circle of radius 2 is touching both the axes and a circle with centre (6, 5). The distance between their centres is
If \(\frac{1}{x(x+1)(x+2)\ldots(x+n)} = \frac{A_0}{x} + \frac{A_1}{x+1} + \frac{A_2}{x+2} + \ldots + \frac{A_n}{x+n}\) then \(A_r\) is equal to
If \(PQ\) is a double ordinate of the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) such that \(OPQ\) is an equilateral triangle, \(O\) being the centre of the hyperbola, then the eccentricity \(e\) of the hyperbola satisfies
\(\sum_{k=0}^{10} {}^{20}C_k\) is equal to
A circle touches the x-axis and also touches the circle which centre at \( (0, 3) \) and radius 2. The locus of the center of the circle is
If the circle \( x^2 + y^2 + 2gx + 2fy + c = 0 \) is touched by \( y = x \) at \( P \) such that \( OP = 6\sqrt{2} \), then the value of \( c \) is
The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line \( y - 4x + 3 = 0 \), is:
The point \( (3, -4) \) lies on both the circles \( x^{2} + y^{2} - 2x + 8y + 13 = 0 \) and \( x^{2} + y^{2} - 4x + 6y + 11 = 0 \). Then, the angle between the circles is
The equation of the circle which passes through the origin and cuts orthogonally each of the circles \( x^{2} + y^{2} - 6x + 8 = 0 \) and \( x^{2} + y^{2} - 2x - 2y = 7 \) is
If the circle \( x^{2} + y^{2} = a^{2} \) intersects the hyperbola \( xy = c^{2} \) in four points \( (x_i, y_i) \), for \( i = 1, 2, 3, 4 \), then \( y_{1} + y_{2} + y_{3} + y_{4} \) equals
The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are
The locus of centre of a circle which passes through the origin and cuts off a length of 4 unit from the line $x=3$ is
The diameters of a circle are along $2x+y-7=0$ and $x+3y-11=0$. Then, the equation of this circle, which also passes through (5, 7), is
The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle 36° is
The area (in square unit) of the circle which touches the lines $4x+3y=15$ and $4x+3y=5$ is
The radius of the circle \( x^{2} + y^{2} - 4x + 6y - 12 = 0 \) is: