Let 2x2 + y2 – 3xy = 0 Be The Equation Of A Pair Of Tangents Drawn From The Origin O to A Circle Of Radius 3 With Centre In The First Quadrant. If A is One Of The Points Of Contact, Find The Length Of OA.

Find the equation of the circle circumscribing the quadrilateral formed by the lines in order are 5x + 3y – 9 = 0, x – 3y = 0, 2x – y = 0, x + 4y – 2 = 0 without finding the vertices of quadrilateral.

Find the equation of a circle which touches the x-axis and the line 4x – 3y+ 4 = 0. Its centre lies in the third quadrant and lies on the line x – y – 1 = 0.

Find the equations of the circle which passes through the origin and cut off chords of length a from each of the lines y = x and y = –x.

Determine the radius of the circle, two of whose tangents are the lines 2x+ 3y – 9 = 0 and 4x + 6y + 19 = 0.

Find the equation of the circle which touches the circle

x² + y² – 6x + 6y + 17 = 0 externally and to which the lines

x² – 3xy – 3x + 9y = 0 are normals.

Find the equation of a circle which passes through the point

(2, 0) and whose centre is the limit of the point of intersection of the lines 3x + 5y = 1and (2 + c)x + 5c²y = 1as c → 1.

Tangents are drawn from P (6, 8) to the circle x² + y² = r². Find the radius of the circle such that the areas of the âˆ† formed by tangents and chord of contact is maximum.

Find the radius of smaller circle which touches the straight line 3x – y = 6 at (1, –3) and also touches the line y = x.

2x – y + 4 = 0 is a diameter of the circle which circumscribed a rectangleABCD. If the co-ordinates of A and B are A(4, 6) and B(1, 9), find the area of rectangle ABCD.

If the circle C₁, x² + y² = 16 intersects another circle C₂ of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to (3/4), find the co-ordinates of centre C₂.