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BITSAT 2011

Exam: BITSAT
Year: 2011
Subject: Mathematics
Chapter: Circle

BITSAT 2011 · Mathematics · Circle

If the lines 3 x-4 y+4=0 and 6 x-8 y-7=0 are tangents to a circle,...

If the lines

3 x-4 y+4=0

and

6 x-8 y-7=0

are tangents to a circle, then the radius of the circle is

Options

A $3 / 2$
B $3 / 4$
C $1 / 10$
D $1 / 20$

Correct answer

B. $3 / 4$

Step-by-step solution

The diameter of the circle is perpendicular distance between the parallel lines (tangents)

3 x-4 y+4=0

and (3 x-4 y-

\frac{7}{2}=

0) and so it is equal to (

\frac{4}{\sqrt{9+16}}+\frac{7 / 2}{\sqrt{9+16}}=\frac{3}{2}

). Hence radius is (

\frac{3}{4}

)

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