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A straight line passes through the point `(alpha,beta)` and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is `x/(2alpha)+y/(2beta)=1.`

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To show that the equation of the straight line passing through the point \((\alpha, \beta)\) and bisecting the portion of the line intercepted between the axes is given by \(\frac{x}{2\alpha} + \frac{y}{2\beta} = 1\), we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Intercepts**: Let the x-intercept of the line be \(a\) and the y-intercept be \(b\). Therefore, the intercepts can be represented as the points \((a, 0)\) and \((0, b)\). 2. **Midpoint Condition**: ...
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RD SHARMA-THE STRAIGHT LINES -Solved Examples And Exercises
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  11. Find the equations of the straight lines which pass through the origin...

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  12. find the equation of the straight line passing through (2,1) and bisec...

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  13. Find the equation of the straight line passing through the origin and ...

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  14. Find the equation of the straight line which is at a distance 3 from ...

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  15. the length of the perpendicular from the origin to a line is 7 and a l...

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  16. Find the equation of the straight line upon which the length of perp...

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  17. Find the equation of a line for which: p=5,alpha=60^@

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  18. Find the equation of a line for which: p=8,alpha=225^@

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  19. Find the equation of a line for which: p=8,alpha=300^@

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  20. Find the equation of the line whose perpendicular distance from the ...

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