Question

A point A is at a distance of under root 10 from the point (4,3).Find the co-ordinate of point A. if it's ordinate is twice of its abscissa.

Answer 1

Hope this will be helpful for you

Answer 2

Step-by-step explanation:

$Let \: B(4,3) = (x_{1},y_{1}) \: and \\ A(a ,2a) = (x_{2},y_{2})$

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

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

$BA = \sqrt{10} \:(given)$

$\implies BA^{2} = 10$

$\implies (a-4)^{2} + (2a-3)^{2} = 10$

$\implies a^{2} - 2\times a\times 4 +4^{2} (2a)^{2}-2\times 2a\times 3+3^{2} = 10$

$\implies a^{2} - 8a + 16 +4a^{2} -12a + 9 - 10 = 0$

$\implies 5a^{2} -20a +15 = 0$

/* Divide each term by 5 , we get

$\implies a^{2} - 4a + 3 = 0$

/* Splitting the middle term, we get

$\implies a^{2} - 1a - 3a + 3 = 0$

$\implies a(a-1) -3(a-1) = 0$

$\implies (a-1)(a-3) = 0$

$\implies a - 1 = 0 \:Or \: a - 3 = 0$

$\implies a = 1 \:Or \: a = 3$

Case 1:

If a = 1 then A(a,2a) = ( 1,2)

case 2:

If a = 3 then A(a,2a) = (3,6)

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