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391.
If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.

Given, P(x,y) is equidistant from A(5,1) and B(-1,5)

Now, AP = BP

$\Rightarrow \sqrt{{(5 - x)}^{2} + {(1 - y)}^{2}} = \sqrt{{(- 1 - x)}^{2} + {(5 - y)}^{2}} \Rightarrow {(5 - x)}^{2} + {(1 - y)}^{2} = {(- 1 - x)}^{2} + {(5 - y)}^{2} \Rightarrow (25 + x^{2} - 10 x) + (1 + y^{2} - 2 y) = (1 + x^{2} + 2 x) + (25 + y^{2} - 10 y) \Rightarrow x^{2} + y^{2} - 10 x - 2 y + 26 = x^{2} + y^{2} + 2 x - 10 y + 26 \Rightarrow - 10 x - 2 y = - 10 y + 2 y \Rightarrow - 12 x = - 8 y \Rightarrow 3 x = 2 y . . . . . . . . . (Dividing throughout by - 4)$

Long Answer Type

392.

In what ratio does the point $(\frac{24}{11}, y)$ divides the line segment joining the points P(2, -2) and Q(3, 7)? Also find the value of y.

Multiple Choice Questions

393.

The coordinates of the point P dividing the line segment joining the points A(1, 3) and B(4, 6) in the ratio 2 : 1 are

( 2, 4 )
( 3, 5 )
( 4, 2 )
( 5, 3 )

394.

If the coordinates of the one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then the coordinates of the other end of the diameter are:

( -6, 7)
( -6, -7)
( 6,7)
( -6, -7)

Short Answer Type

395.

If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5) then find the value of p.

Long Answer Type

396.

A point P divides the line segment joining the points A(3,-5) and B(-4, 8) such that $\frac{AP}{PB} = \frac{K}{1}$ . If P lies on the line x + y = 0, then find the value of K.