## Question

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

### Solution

The given tangents are

2*x* + 3*y* – 9 = 0 …(1)

and 4*x* + 6*y* + 19 = 0

Which are parallel, then distance between parallel tangents must be diameter of the circle. Then diameter

#### SIMILAR QUESTIONS

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 *x*^{2} + *y*^{2} + 16*x* – 24*y* + 183 = 0 by the line mirror 4*x* + 7*y* + 13 = 0.

Find the area of the triangle formed by the tangents drawn from the point (4, 6) to the circle *x*^{2} + *y*^{2} = 25 and their chord of contact. Also find the length of chord of contact.

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Find the lengths of common tangents of the circles *x*^{2} + *y*^{2} = 6*x* and *x*^{2} +*y*^{2} + 2*x* = 0. * *

Find the equation of the circle circumscribing the triangle formed by the lines:

*x* + *y* = 6, 2*x* + *y* = 4 and *x* + 2*y* = 5,

Without finding the vertices of the triangle.

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

Find the equation of a circle which touches the *x*-axis and the line 4*x* – 3*y*+ 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

*x*^{2} + *y*^{2} – 6*x* + 6*y* + 17 = 0 externally and to which the lines

*x*^{2} – 3*xy* – 3*x* + 9*y* = 0 are normals.