(B) Let the line be $L(x, y) = 3x - 5y + a = 0$. For two points $(x_1, y_1)$ and $(x_2, y_2)$ to lie on the same side of the line $Ax + By + C = 0$,th

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(B) Let the line be $L(x, y) = 3x - 5y + a = 0$. For two points $(x_1, y_1)$ and $(x_2, y_2)$ to lie on the same side of the line $Ax + By + C = 0$,the values $L(x_1, y_1)$ and $L(x_2, y_2)$ must have the same sign,i.e.,$L(x_1, y_1) \times L(x_2, y_2) > 0$. For point $(1, 2)$,$L(1, 2) = 3(1) - 5(2) + a = a - 7$. For point $(3, 4)$,$L(3, 4) = 3(3) - 5(4) + a = a - 11$. Thus,we require $(a - 7)(a - 11) > 0$. This inequality holds when $a 11$.

Class 11 Mathematics Straight Line Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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Find the set of all values of $a$ such that both the points $(1, 2)$ and $(3, 4)$ lie on the same side of the line $3x - 5y + a = 0$.

AP EAMCET 2017 All AP EAMCET

A
$a > 11$
B
$a > 11 \cup a < 7$
C
$a < 7$
D
$\phi$

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Straight Line

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Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

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Find the set of all values of $a$ such that both the points $(1, 2)$ and $(3, 4)$ lie on the same side of the line $3x - 5y + a = 0$.

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