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If non­zero numbers a,b,c are in H.P., then the straight line   \frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0   always passes through a fixed point. That point is

  • Option 1)

    (-1,-2)\;

  • Option 2)

    \; (-1,2)\;

  • Option 3)

    \; \left ( 1,-\frac{1}{2} \right )\;

  • Option 4)

    \; (1,-2)

 

Answers (1)

As we learnt in 

Intercept form of a straight line -

\frac{x}{a}+\frac{y}{b}=1

 

- wherein

a and b are the x-intercept and y -intercept respectively.

 

 

 

Condition of co linearity of three points -

\frac{y_{1}-y_{2}}{x_{1}-x_{2}}=\frac{y_{2}-y_{3}}{x_{2}-x_{3}}

- wherein

The three points are A(x1,y1) , B(x2,y2), C(x3,y3).

 

 If  a, b, c are in H.P

\frac{2}{b}=\frac{1}{a}+\frac{1}{c}

i.e. \frac{1}{a}-\frac{2}{b}+\frac{1}{c}=0

Comparing with

\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0

(x=1, y=-2)

Line always passes through (1, -2)


Option 1)

(-1,-2)\;

Incorrect option    

Option 2)

\; (-1,2)\;

Incorrect option    

Option 3)

\; \left ( 1,-\frac{1}{2} \right )\;

Incorrect option    

Option 4)

\; (1,-2)

Correct option

Posted by

Vakul

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