Home
Class 11
MATHS
If p is the perpendicualr distance of th...

If p is the perpendicualr distance of the origin from the line whose intercepts on the axes are a and b, show that
`1/(p^(2))=1/(a^(2))+1/(b^(2))`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • THE STRAIGHT LINE

    ICSE|Exercise EXERCISE 16 (g)|13 Videos
  • THE STRAIGHT LINE

    ICSE|Exercise EXERCISE 16 (h)|11 Videos
  • THE STRAIGHT LINE

    ICSE|Exercise EXERCISE 16 (e)|14 Videos
  • STRAIGHT LINES

    ICSE|Exercise Multiple Choice Questions |46 Videos
  • TRIGONOMETRIC FUNCTION

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS |44 Videos

Similar Questions

Explore conceptually related problems

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/(p^2)=1/(a^2)+1/(b^2) .

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/(p^2)=1/(a^2)+1/(b^2) .

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/(p^2)=1/(a^2)+1/(b^2) .

The tngent of angle between the lines whose intercepts on the axes are a, -b and b -a respectively is

Find the distance of the point P from the line l in that : l: x/a - y/b = 1 and P-= (b, a)

If the length of perpendicular from origin to the line ax+by+a+b=0 is p , then show that : p^(2)-1=(2ab)/(a^(2)+b^(2))

If p is the length of perpendicular from the origin on the line (x)/(a)+(y)/(b)=1 and a^(2) , p^(2) and b^(2) are in AP, the show that a^(4)+b^(4)=0 .

If p be the length of the perpendicular from the origin on the line x//a+y//b =1, then p^2=a^2+b^2 b. p^2=1/(a^2)+1/(b^2) c. 1/(p^2)=1/(a^2)+1/(b^2) d. none of these

If 2a^2 - 7ab -ac +3b^2-2bc-c^2=0 then the family of lines ax + by + c=0 are either concurrent at the point P(x_1,y_1) or at the point Q(x_2, y_2) . Find the distance of the origin from the line passing through the points P and Q, the distance being measured parallel to the line 3x-4y=2 .

If a plane has intercepts a, b and c on the coordinate axes and is at a distance of p units from the origin, prove that they (1)/(a^(2))+(1)/(b^(2))+(1)/(c^(2))=(1)/(p^(2))