List of top Mathematics Questions on Circles asked in MET

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is

The locus of the point \(P(x, y)\) satisfying \(\sqrt{(x-3)^2 + (y-1)^2} + \sqrt{(x+3)^2 + (y-1)^2} = 6\) is

The equation of the parabola whose vertex is (-1, -2), axis is vertical and which passes through the point (3, 6), is

The length of the axis of the conic \(9x^2 + 4y^2 - 6x + 4y + 1 = 0\) are

The normal at the point (3, 4) on a circle cuts the circle at the point (-1, -2). Then the equation of the circle is

The difference of the focal distances of any point on the hyperbola is equal to its

The locus of the point of intersection of two perpendicular tangents to a circle is called

Consider the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the area of the triangle formed by the asymptotes and the tangent drawn to it at $(a,0)$ is

The equation of the circle passing through the point \((2a, 0)\) and whose radical axis is \(x = \frac{a}{2}\) with respect to the circle \(x^2 + y^2 = a^2\), will be

The condition that the straight line \(cx - by + b^2 = 0\) may touch the circle \(x^2 + y^2 = ax + by\) is

The locus of the mid-points of the chords of the circle \(x^2 + y^2 = 16\) which are tangent to the hyperbola \(9x^2 - 16y^2 = 144\) is

If $(mᵢ, 1/mᵢ)$ are four distinct points on a circle, then

Consider four circles $(x ± 1)² + (y ± 1)² = 1$, then the equation of smaller circle touching these four circles is

The equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius is

The length of the common chord of the two circles $(x-a)²+(y-b)²=c²$ and $(x-b)²+(y-a)²=c²$ is