Find The Middle Point Of The Chord Intercepted On Line lx + my + n = 0 By The Circle x2 + y2 = a2.  

Find the radius of the smallest circle which touches the straight line 3x– y = 6 at (1, –3) and also touches the line y = x. complete up to one place of decimal.

Let S ≡ x² + y² + 2gx + 2fy + c = 0 be a given circle. find the locus of the foot of the perpendicular drawn from the origin upon any chord of S which subtends a right angle at the origin.

The normal 3x – 4y = 4 and 6x – 8y – 7 = 0 are tangents to the circle. Then its radius is:

The circle x² + y² + x + y = 0 and x² + y² + x – y = 0 intersect at the angle of:

Find the radical centre of the circles, x² + y² + 3x + 2y + 1 = 0,  x² + y² – x + 6y + 5 = 0, x² + y² + 5x – 8y + 15 = 0

The tangents drawn from the origin to the circle x² + y² – 2kx – 2ry + r² = 0 are perpendicular, if:

The locus of the mid points of a chord of the circles x² + y² = 4, which subtends a right angle at the origin is:

The chord of contact of tangents from a point P to a circle passes through Q, if l₁ and l₂ are the lengths of tangents from P and Q to the circle, then PQ is equal to:

Find the equation of the chord of x² + y² – 6x + 10y – 9 = 0 which is bisected at (–2, 4). 

Find the power of the point (2, 4) with respect to the circle. x² + y² – 6x+ 4y – 8 = 0