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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Coordinate Geometry
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If the points (1,1) and (3,5) were to be on the opposite side of the line $3x-5y+a=0$.Find the value of a?

$\begin{array}{1 1}(a)\;a > 2,a < 16\\(b)\;a < 2,a < 15\\(c)\;a > 3,a < 5\\(d)\;a > 5,a < 2\end{array}$

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1 Answer

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For the point (1,1) & (3,5) to be on opposite side.
$\large\frac{f(1,1)}{f(3,5)}$$ < 0$
Where $f(x,y)=3x-5y+a$
$\large\frac{-2+a}{-16+a} $$ < 0$
$\large\frac{a-2}{a-16}$$ < 0$
$a \in (2,16)$
(i.e) $a > 2$ and $a < 16$
Hence (a) is the correct answer.
answered Feb 4, 2014 by sreemathi.v
 

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