Question

The length of the perpendicular segment from the origin to a line is 2 units
and the inclination of this perpendicular is a such that sin a=1/3 where a is acute
acute. Find the equation of the line.
and​

Answer 1

y = - 2√2x  + 6     perpendicular  from the origin to the line is inclined at a such that sin a=1/3 and length = 2 unit

Step-by-step explanation:

Sina = 1/3

=> 1/3  = Perpendicular / hypotenuse

=> 1/3 = P/2

=> P = 2/3

Base = √2² - (2/3)²  = √ 4 - 4/9   = 4√2/3

Hence coordinate of perpendicular segment Touching line

= ( 4√2/3 , 2/3)

Slope of Perpendicular

= (2/3)/(4√2/3)

= 1/2√2

Slope of line  =  -1/1/2√2  = - 2√2

Equation of line

y = - 2√2x  + c

point  ( 4√2/3 , 2/3)

=>  2/3 = - 2√2 * 4√2/3  + c

=> 2/3 = -16/3  + c

=> c = 18/3

=> c = 6

y = - 2√2x  + 6  is Equation of line

Learn More :

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Answer 2

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