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Let (2,1) be a point on line 3x+4y=2.Find the point at distance of 5 units on the line from the given point?
 one year ago
 one year ago
Let (2,1) be a point on line 3x+4y=2.Find the point at distance of 5 units on the line from the given point?
 one year ago
 one year ago

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hartnnBest ResponseYou've already chosen the best response.1
\(\large{distance}(ax+by+c=0, (x_0, y_0)) = \frac{ax_0+by_0+c}{\sqrt{a^2+b^2}}\)
 one year ago

DLSBest ResponseYou've already chosen the best response.2
How can we solve this using parametric form?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
i didn't get your question actually, (2,1) does NOT lie on that line. can u draw a figure or something ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
Distance between points (x1,y1) and (x2,y2) is \(\huge d=\sqrt{(x_1x_2)^2+(y_1y_2)^2}\)
 one year ago

DLSBest ResponseYou've already chosen the best response.2
\[\frac{xx1}{\cos \Theta} = \frac{yy1}{\sin \Theta} = r\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
but,(2,1) does NOT lie on that line.
 one year ago

DLSBest ResponseYou've already chosen the best response.2
3x+4y+66=2 3(x2)=4(y+1) \[\frac{x2}{4/5}\frac{y+1}{3/5}=r=+5 or 5\]
 one year ago

DLSBest ResponseYou've already chosen the best response.2
why did we divide by sqrt of a^2+b^2 that is 5? They say by doing that we get sin Theta and cos Theta
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so that the two numbers(4/5 and 3/5) here satisfy, a^2+b^2=1 which is the property of sin and cos
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so we can take one as 4/5 and other as 3/5
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
like here u take cos t =4/5, sin t = 3/5
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
if you did not divide by 5, then 4^2+3^2 does not equal 1 so u cannot take cos t=4, and sin t =3
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
its like normalization....
 one year ago

DLSBest ResponseYou've already chosen the best response.2
i know that but why did we divide by sqrt of a^2+b^2 only?
 one year ago

DLSBest ResponseYou've already chosen the best response.2
any special logic or anything?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
for any 2 numbers \(\large(\frac{a}{\sqrt{a^2+b^2}})^2+(\frac{b}{\sqrt{a^2+b^2}})^2=1\) so there is a need to divide by sqrt(....)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
what else can u divide those numbers by, to get their sum of squares =1 ?
 one year ago
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