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).
x2 + y2 – 18x – 16y + 120 = 0
The given circle is x2 + y2 – 2x – 4y – 20 = 0
With centre (1, 2) and radius
And required circle has radius 5 hence circles touch each other externally.
Since point of contact is P (5, 5).
∴ P is the mid point of C1 and C2, let co-ordinates of centre C2 is (h, k) then
∴ Equation of required circle is
(x – 9)2 + (y – 8)2 = 52
⇒ x2 + y2 – 18x – 16y + 120 = 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.
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 locus of the mid point of the chord of the circle x2 + y2 = a2which subtend a right angle at the point (p, q).