Determine the radius of the circle, two of whose tangents are the lines 2x+ 3y – 9 = 0 and 4x + 6y + 19 = 0.
The given tangents are
2x + 3y – 9 = 0 …(1)
and 4x + 6y + 19 = 0
Which are parallel, then distance between parallel tangents must be diameter of the circle. Then diameter
Find the equation of the circle which passes through the origin and belongs to the co-axial of circles whose limiting points are (1, 2) and (4, 3).
Find the equation of the image of the circle x2 + y2 + 16x – 24y + 183 = 0 by the line mirror 4x + 7y + 13 = 0.
Find the area of the triangle formed by the tangents drawn from the point (4, 6) to the circle x2 + y2 = 25 and their chord of contact. Also find the length of chord of contact.
Find the lengths of external and internal common tangents to two circlesx2 + y2 + 14x – 4y + 28 = 0 and x2 + y2 – 14x + 4y – 28 = 0.
Find the lengths of common tangents of the circles x2 + y2 = 6x and x2 +y2 + 2x = 0.
Find the equation of the circle circumscribing the triangle formed by the lines:
x + y = 6, 2x + y = 4 and x + 2y = 5,
Without finding the vertices of the triangle.
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.
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.