Question

a relation between a and b such that point (a, b )is equidistant from the points (8,3) and (2,7 )is​

Answer 1

Answer:

Step-by-step explanation:

The distance between (8,3) and (a,b) is equal to the distance between (2,7) and (a,b)

√((8-a)^2 + (3-b)^2) = √((2-a)^2 + (7-b)^2)

On squaring both sides and simplifying we get,

73-53= -4a - 14b + 16a + 6b

20= 12a - 8b

This is equal to

3a- 2b = 5

Hope this helps.

Answer 2

Answer:

$\red { Relation \: between \:a \:and \:b }$

$\green{ 3a-2b = 5 }$

Step-by-step explanation:

$Let \:P(a,b) \;is \: equidistant \: from \:the \\points \:A(8,3)\: and \: B(2,7)$

$\underline { \blue {By \: distance \: formula }}$

$\boxed {\pink { Distance = \sqrt{(x_{2}-x_{1})^{2}+{(y_{2}-y_{1})^{2}}}}}$

$PA = PB$

$\implies PA^{2} = PB^{2}$

$\implies (a-8)^{2} + (b-3)^{2} = (a-2)^{2} + (b-7)^{2}$

$\implies a^{2}-16a+64 + b^{2}-6b+9 \\= a^{2} -4a+4 + b^{2}-14b+49$

$\implies -16a - 6b +73 = -4a - 14b + 53$

$\implies 73 - 53 = -4a + 16a -14b + 6b$

$\implies 20 = 12a - 8b$

/* Divide each term by 4, we get

$\implies 5 = 3a - 2b$

Therefore.,

$\red { Relation \: between \:a \:and \:b }$

$\green{ 3a-2b = 5 }$

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