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  • The locus of centre of a circle touching the lines <img alt="\mathrm{3 x+4 y=5\, \& \, 6 x+8 y=5}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x&plus;4%20y%3D5%5C%2

The locus of centre of a circle touching the lines \mathrm{3 x+4 y=5\, \& \, 6 x+8 y=5} is

Option: 1

\mathrm{3 x+4 y=0}


Option: 2

\mathrm{3 x+4 y=5 / 2}


Option: 3

\mathrm{12 x+16 y=15}


Option: 4

\mathrm{\text { none of these }}


Answers (1)

best_answer

Tangents are \mathrm{3 x+4 y=5} and \mathrm{3 x+4 y=5 / 2.}

Centre will always lie on a straight line equidistant from given lines. Straight line is of the from \mathrm{3 x+4 y=\lambda}

\mathrm{ \lambda=\frac{c_1+c_2}{2}=\frac{5+5 / 2}{2}=\frac{15}{4} }

'c' is correct

Posted by

vishal kumar

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