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.
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.
The circle x2 + y2 = 1 cuts the x-axis at P and Q. another circle with centre at Q and variable radius intersects the first circle at R above the x-axis and the line segment PQ at S. Find the maximum area of the triangleQSR.
Find the equation of a circle having the lines x2 + 2xy + 3x + 6y = 0 as its normals and having size just sufficient to contain the circle
x(x – 4) + y(y – 3) = 0.
Find the equation of the circle whose radius is 5 and which touches the circle
x2 + y2 – 2x – 4y – 20 = 0 at the point (5, 5).
Find the locus of the mid point of the chord of the circle x2 + y2 = a2which subtend a right angle at the point (p, q).
Let a circle be given by
2x (x – a) + y(2y – b) = 0 (a ≠ 0, b ≠ 0)
Find the condition on a and b if two chords, each bisected by the x-axis, can be drawn to the circle from (a, b/2).
The centre of the circle S = 0 lie on the line 2x – 2y + 9 = 0 and S = 0 cuts orthogonally the circle x2 + y2 = 4. Show that circle S = 0 passes through two fixed points and find their co-ordinates.
be a given circle. Find the locus of the foot of perpendicular drawn from origin upon any chord of Swhich subtends a right angle at the origin.
P is a variable on the line y = 4. Tangents are drawn to the circle x2 + y2= 4 from P to touch it at A and B. The perpendicular PAQB is completed. Find the equation of the locus of Q.