If y+(2p+1)x+3=0 and 8y-(2p-1)x=5 are mutually perpendicular.  Find the values of p.

Asked by sonali | 23rd Feb, 2018, 11:19: AM

Expert Answer:

begin mathsize 16px style Slope space of space the space line space left parenthesis 2 straight p plus 1 right parenthesis straight x plus straight y plus 3 equals 0 space is space minus left parenthesis 2 straight p plus 1 right parenthesis.
Slope space of space the space line space minus left parenthesis 2 straight p minus 1 right parenthesis straight x plus 8 straight y equals 5 space is space fraction numerator left parenthesis 2 straight p minus 1 right parenthesis over denominator 8 end fraction.
According space to space the space question
Product space of space slopes space equals space minus 1
open square brackets negative left parenthesis 2 straight p plus 1 right parenthesis close square brackets fraction numerator space left parenthesis 2 straight p minus 1 right parenthesis over denominator 8 end fraction equals negative 1
4 straight p squared minus 1 equals 8
4 straight p squared equals 9
straight p equals plus-or-minus 3 over 2
end style

Answered by Sneha shidid | 23rd Feb, 2018, 11:45: AM