Answer
397.2k+ views
Hint: In the given solution, it is given that the point on the two sides, we have to take the negative side (2nd quadrant) and positive side (1st quadrant) lines, then we have to combine them to get the value of y.
The following is the schematic diagram to determine The coordinates of the foot.
Complete step-by-step answer:
Given:
The point on the line is P.
The line one side is $y+\sqrt 3 x=2$ assuming as equation 1
The distance at which the point intersects the line is \[x = 5\] units.
The line on another side is $y-\sqrt 3 x=2$ assuming as equation 2
Solving equation 1 and 2, we get,
\[
\Rightarrow y - \sqrt 3 x + y + \sqrt 3 x = 2 + 2\\
2y = 4\\
y = 2
\]
It means the value of y is 2.
The equation to find the coordinates of the point P,
\[P = (x\sin \theta ,\,y + x\cos \theta )\]
Here, \[\theta \] is the angle that the line is formed by touching the y-axis. It can be taken as \[30^\circ \]
Substituting the values in the above equation, then we will get
\[
\Rightarrow P = \pm (x\sin \theta ,\,y + x\cos \theta )\\
= \pm \left( {5\sin 30^\circ ,\,2 + 5\cos 30^\circ } \right)\\
= \pm \left( {\dfrac{{5\sqrt 3 }}{2},2 + \dfrac{{5\sqrt 3 }}{2}} \right)
\]
So the coordinates of the foot perpendicular to the point P on the bisector of angle can be taken as y-axis then the coordinates will be \[\left( {0,\dfrac{{4 + 5\sqrt 3 }}{2}} \right)\] .
Therefore, the coordinates of the foot of the perpendicular from P on the bisector of the angle between them are \[\left( {0,\dfrac{{4 + 5\sqrt 3 }}{2}} \right)\]
So, the correct answer is “ \[\left( {0,\dfrac{{4 + 5\sqrt 3 }}{2}} \right)\] ”.
Note: While solving the problem, we have to consider y-axis and x-axis coordinate value will become zero because the point p will lie on the y-axis line and a line should be drawn parallel to x-axis, which will be 0.
The following is the schematic diagram to determine The coordinates of the foot.
![seo images](https://www.vedantu.com/question-sets/1a5c6f0b-5194-4dff-84d3-691d5fc095403233711163722719543.png)
Complete step-by-step answer:
Given:
The point on the line is P.
The line one side is $y+\sqrt 3 x=2$ assuming as equation 1
The distance at which the point intersects the line is \[x = 5\] units.
The line on another side is $y-\sqrt 3 x=2$ assuming as equation 2
Solving equation 1 and 2, we get,
\[
\Rightarrow y - \sqrt 3 x + y + \sqrt 3 x = 2 + 2\\
2y = 4\\
y = 2
\]
It means the value of y is 2.
The equation to find the coordinates of the point P,
\[P = (x\sin \theta ,\,y + x\cos \theta )\]
Here, \[\theta \] is the angle that the line is formed by touching the y-axis. It can be taken as \[30^\circ \]
Substituting the values in the above equation, then we will get
\[
\Rightarrow P = \pm (x\sin \theta ,\,y + x\cos \theta )\\
= \pm \left( {5\sin 30^\circ ,\,2 + 5\cos 30^\circ } \right)\\
= \pm \left( {\dfrac{{5\sqrt 3 }}{2},2 + \dfrac{{5\sqrt 3 }}{2}} \right)
\]
So the coordinates of the foot perpendicular to the point P on the bisector of angle can be taken as y-axis then the coordinates will be \[\left( {0,\dfrac{{4 + 5\sqrt 3 }}{2}} \right)\] .
Therefore, the coordinates of the foot of the perpendicular from P on the bisector of the angle between them are \[\left( {0,\dfrac{{4 + 5\sqrt 3 }}{2}} \right)\]
So, the correct answer is “ \[\left( {0,\dfrac{{4 + 5\sqrt 3 }}{2}} \right)\] ”.
Note: While solving the problem, we have to consider y-axis and x-axis coordinate value will become zero because the point p will lie on the y-axis line and a line should be drawn parallel to x-axis, which will be 0.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)