If a point P(x,y) is the equidistant from the points A(2,3) and B(6,1), find the equation of locus of moving point P.​



please answer it and I will mark your answer as the brainliest..please..!!!

Answers

Answer 1

Answer:

[tex]y=2x-6[/tex]

Step-by-step explanation:

A locus can be defined as a curve or figure formed by all the points satisfying a particular equation of the relation between coordinates.

The condition stated in the question is such that a generic (x,y) point of the curve is equidistant from the points A(2,3) and B(6,1).

The distance d1 from (x,y) to (2,3) is:

[tex]d_1=\sqrt{(x-2)^2+(y-3)^2}[/tex]

The distance d2 from (x,y) to (6,1) is:

[tex]d_2=\sqrt{(x-6)^2+(y-1)^2}[/tex]

Since d1=d2:

[tex]\sqrt{(x-2)^2+(y-3)^2}=\sqrt{(x-6)^2+(y-1)^2}[/tex]

Squaring both sides:

[tex](x-2)^2+(y-3)^2=(x-6)^2+(y-1)^2[/tex]

Operating:

[tex]x^2-4x+4+y^2-6y+9=x^2-12x+36+y^2-2y+1[/tex]

Simplifying all the squares:

[tex]-4x+4x+4-6y+9=-12x+36-2y+1[/tex]

Moving the variables to the left side and the numbers to the right side:

[tex]-4x+12x-6y+2y=36+1-4-9[/tex]

Simplifying:

[tex]8x-4y=24[/tex]

Dividing by 4:

[tex]2x-y=6[/tex]

Or, equivalently:

[tex]\boxed{y=2x-6}[/tex]


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Answers

Answer:

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can i get a thanks and brainliest please?

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tadah!!

Hope that helps.

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Step-by-step explanation:

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Step-by-step explanation:

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The attachment shows what the graphs of the choices look like.

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Step-by-step explanation:

hope this helps :)

Answer:

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i think its D????????????????????????


5x5 = 25
9 x 4 = 36
- and a + equals a -



Answer: The answer is A, (5x+6)(5x-6)

Step-by-step explanation: The negative and positive 6 will cancel out the regular X, meaning that 25x^2 and -36 are the only numbers left.

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