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If p is the length of perpendicular from...

If `p` is the length of perpendicular from point `(1,1)` to the straight line `ax+by+a+b=0`, then prove that :
`p^(2)=4+(8ab)/(a^(2)+b^(2))`

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To prove that the length of the perpendicular \( p \) from the point \( (1, 1) \) to the straight line \( ax + by + a + b = 0 \) satisfies the equation \( p^2 = 4 + \frac{8ab}{a^2 + b^2} \), we will follow these steps: ### Step 1: Identify the line and point The line is given by the equation: \[ ax + by + a + b = 0 \] and the point is \( P(1, 1) \). ...
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NAGEEN PRAKASHAN ENGLISH-STRAIGHT LINES-Exercise
  1. If p is the length of perpendicular from point (1,1) to the straight l...

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  2. Find the new co-ordinates of the following points when origin is shift...

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  3. At which point the origin should be shifted such that the new co-ordin...

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  4. If the origin is shifted to the point (1,2) then what will be the tran...

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  5. Find the point at which origin is shifted such that the transformed e...

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  6. Find the point at which is shifted such that the transformed equations...

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  7. Shift the origin to a suitable point so that the equation y^2+4y+8x-2=...

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  8. Show that the area of triangle whose vertices are (1,0), (2,4) and (3,...

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  9. Find the slope of the lines whose iclination is given : (i) 45^(@) (...

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  10. Find the inclination of the lines whose slopes are as follows : (i) ...

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  11. Find the slopes of the lines passing through the following points : ...

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  12. If the slope of a line passing through the points (1,4) and (x,2) is 2...

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  13. If the angle of inclination of line joining the points (x,3) and (-2,5...

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  14. If the slop of line joining the points (6,-3) and (x,7) is 2, find the...

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  15. Show that the line joining the points (4,-1) and (-3,3) is parallel to...

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  16. If the line joining the points (5,y) and (4,9) is parallel to the line...

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  17. Show that the line joining the points (4,-3) and (0,7) is perpendicula...

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  18. If the line joining the points (6,-2) and (8,4) is perpendicular to th...

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  19. Without using Pythagoras theorem, show that A(4,4),\ B(3,5)a n d\ C(-1...

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  20. Using slopes, show that the points A(0,5), B(3,2) and C(-1,6) are coll...

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  21. Using the slope of line, show that the points (-1,-2), (0,4), (3,3) an...

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