Circle PYQs - Last 5 Years

Let all the points on the curve $x^2+y^2-10 x=0$ are reflected about the line $y=x+3$. If the locus of the reflected points is in the form $x^2+y^2+g x+f y+c=0$, then the value of $(g+f+c)$ is

The number of common tangents to the circles $x^2+y^2-4 x-6 y-12=0, x^2+y^2+6 x+18 y+26=0$ is

Let $x-y=0$ and $x+y=1$ be two perpendicular diameters of a circle of radius $R$. The circle will pass through the origin if $R$ is equal to

If two circles which pass through the points \((0, a)\) and \((0,-a)\) and touch the line \(\mathrm{y}=\mathrm{m} x+\mathrm{c}\), cut orthogonally then

Chords \(\mathrm{AB}\) & \(\mathrm{CD}\) of a circle intersect at right angle at the point \(\mathrm{P}\). If the length of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle is

Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of the flower bed be greatest?

A straight line meets the co-ordinate axes at A and B. A circle is circumscribed about the triangle OAB, O being the origin. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the d...

Two circles \({S_1} = p{x^2} + p{y^2} + 2g'x + 2f'y + d = 0\) and \({S_2} = {x^2} + {y^2} + 2gx + 2fy + d' = 0\) have a common chord PQ. The equation of PQ is

The side AB of \(\Delta\)ABC is fixed and is of length 2a unit. The vertex moves in the plane such that the vertical angle is always constant and is \(\alpha\). Let x-axis be along AB and the origin be at A. Then the locus of the vertex is

If the equation of one tangent to the circle with centre at (2, \(-\)1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is

A curve passes through the point (3, 2) for which the segment of the tangent line contained between the co-ordinate axes is bisected at the point of contact. The equation of the curve is