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willasiacochran
08.12.2019 •
Mathematics
Find the slope of the line perpendicular to the line x cos alpha + y sin alpha = p
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Ответ:
The slope of the line perpendicular to the line x cos α + y sin α = p is tanα .
Step-by-step explanation:
Given equation of line as :
x cos α + y sin α = p
The standard equation of line is given as
y = m x + c
where m is the slope of the line
Now, for line x cos α + y sin α = p
Or, y sin α = p - x cos α
or, y sin α = - x cos α + p
Or, y = -
x + ![\dfrac{\textrm p}{\textrm sin\alpha }](/tpl/images/0409/0783/432e3.png)
Or, y = - cotα x +p cosecα
So By comparing the line, the slope of this line = m = - cotα
Now, when two lines are perpendicular then
The product of the slope of lines = - 1
Let the slope of other line = M
So, from property
m × M = - 1
∴ M =![\frac{-1}{m}](/tpl/images/0409/0783/c90a1.png)
Or, M =![\frac{-1}{-cot\alpha }](/tpl/images/0409/0783/6172c.png)
∴ M = tanα
So, slope of line perpendicular to given line = M = tanα
Hence The slope of the line perpendicular to the line x cos α + y sin α = p is tanα . Answer
Ответ:
Step-by-step explanation:if ab it s 13 and bc is 21 that means you simplified that and you will get 34