Home
Class 10
MATHS
If p is the length of perpendicular from...

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`

Text Solution

Verified by Experts

Equation of line
`(x)/(a)+(y)/(b)=1implies(x)/(a)+(y)/(b)-1=0`
Length of perpendicular drawn from origin to this line is,
`p=|(0+0-1)/(sqrt((1)/(a^(2))+(1)/(b^(2))))|`
`implies p^(2)=(1)/((1)/(a^(2))+(1)/(b^(2)))implies (1)/(p^(2))=(1)/(a^(2))+(1)/(b^(2))`
Promotional Banner

Similar Questions

Explore conceptually related problems

If p is the length of the perpendicular from the origin on the line whose intercepts on the axes are a and b, then

If p is the length of the perpendicular from the origin on the line whose intercepts on the axes are a and b, then-

If p is 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 origin to the line whose intercepts on the axes are 'a' and 'b' then prove that (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

If p be the measure of the perpendicular segment from the origin on the line whose intercepts on the axis are a and b show that 1/p^2= 1/a^2 + 1/b^2

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))

If p is the length of perpendicular from the origin onto the plane whose intercepts on the axes area a,b,c then (A) a+b+c=p (B) a^-2+b^-2+c^-2=p^(-2) (C) a^(-1)+b^(-1)+c^(-1)=p^(-1) (D) a^(-1)+b^(-1)+c^(-1)=1

If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p , then (A) a^2+b^2=p^2 (B) a^2+b^2=1/p^2 (C) 1/a^2+1/b^2=2/p^2 (D) 1/a^2+1/b^2=1/p^2