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The line segment joining the points \[P(3,3)\] and \[Q(6, - 6)\] is trisected by the points \[A\] and \[B\] such that \[A\] is nearer to \[P\]. If \[A\] also lies on the line given by \[2x\ + \ y\ + \ k\ = \ 0\] , find the value of \[k\].

If the intercept of a line between coordinate axes is divided by the point (-5, 4) in the ratio \[1:2\], then find the equation of the line.

A tangent drawn to the curve $y = f\left( x \right)$ at $p\left( {x,y} \right)$ cuts the $x - axis$ and $y - axis$ at ${\text{A and B}}$ respectively such that ${\text{BP : AP = 3 : 1}}$ given that $f\left( 1 \right) = 1,$ then;

$\left( 1 \right){\text{ Equation of the curve is }}x\left( {\dfrac{{dy}}{{dx}}} \right) - 3y = 0$

$\left( 2 \right){\text{ Normal at }}\left( {1,1} \right){\text{ is }}x + 3y = 4$

$\left( 3 \right){\text{ Curve passes through }}\left( {2,\dfrac{1}{8}} \right)$

$\left( 4 \right){\text{ Equation of the curve is }}x\left( {\dfrac{{dy}}{{dx}}} \right) + 3y = 0$

$\left( 5 \right){\text{ 3 and 4}}$

$\left( 1 \right){\text{ Equation of the curve is }}x\left( {\dfrac{{dy}}{{dx}}} \right) - 3y = 0$

$\left( 2 \right){\text{ Normal at }}\left( {1,1} \right){\text{ is }}x + 3y = 4$

$\left( 3 \right){\text{ Curve passes through }}\left( {2,\dfrac{1}{8}} \right)$

$\left( 4 \right){\text{ Equation of the curve is }}x\left( {\dfrac{{dy}}{{dx}}} \right) + 3y = 0$

$\left( 5 \right){\text{ 3 and 4}}$

The straight line $3x + y = 9$ divides the line segment joining the points $\left( {1,3} \right)$ and $\left( {2,7} \right)$ in the ratio:

(A) $3:4$ externally

(B) $3:4$ internally

(C) $4:5$ internally

(D) $5:6$ externally

(A) $3:4$ externally

(B) $3:4$ internally

(C) $4:5$ internally

(D) $5:6$ externally

The mid-point of the line joining the points $\left( { - 10.8} \right){\text{ and }}\left( { - 6,12} \right)$ divides the line joining the points $\left( {4, - 2} \right){\text{ and }}\left( { - 2,4} \right)$ in the ratio:

$\left( 1 \right)1:2{\text{ internally}}$

$\left( 2 \right)1:2{\text{ externally}}$

$\left( 3 \right)2:1{\text{ internally}}$

$\left( 4 \right)2:1{\text{ externally}}$

$\left( 5 \right)2:3{\text{ externally}}$

$\left( 1 \right)1:2{\text{ internally}}$

$\left( 2 \right)1:2{\text{ externally}}$

$\left( 3 \right)2:1{\text{ internally}}$

$\left( 4 \right)2:1{\text{ externally}}$

$\left( 5 \right)2:3{\text{ externally}}$

In what ratio are the joining points $(3, - 6)$ and $( - 6,8)$ divided by the $y$- axis?

If $2a + 3b - 5c = 0$ , then the ratio in which $c$ divides $AB$ is ?

A) 3:2 internally

B) 3:2 externally

C) 2:3 internally

D) 2:3 externally

A) 3:2 internally

B) 3:2 externally

C) 2:3 internally

D) 2:3 externally

Find the ratio in which the line segment joining the points\[\left( { - 3,10} \right)\] and \[\left( {6, - 8} \right)\] is divided by \[\left( { - 1,6} \right)\].

In what ratio does the point (-4,6) divide the line segment joining the points $A\left( { - 6,10} \right)$ and $B\left( {3, - 8} \right)$.

If A (-14, -10), B (6, -2) is given, find the coordinates of the points which divide segment AB into four equal parts?

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6)?

Find the ratio in which the join of the points $ \left( {1,2} \right) $ and $ \left( { - 2,3} \right) $ is divided by the line $ 3x + 4y = 7 $

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