Determine the radius of the circle, two of whose tangents are the lines 2x+3y-9

Question

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

Options:

A . 134√37

B . 354√13

C . 114√13

D . 374√13

Answer: Option D
:
D
The given tangents are
2x+3y-9 = 0
4x+6y+19 =0
Or 2x + 3y +

\frac{19}{2}

= 0
Which are parallel, than distance between parallel tangents must be diameter of the circle than diameter.

\frac{∣ ∣ ∣ \frac{19}{2} - (- 9) ∣ ∣ ∣}{\sqrt{2^{2} + 3^{2}}} = \frac{37}{2 \sqrt{13}}

Radius =

\frac{1}{2}

diameter =

\frac{37}{4 \sqrt{13}}

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