64
If the point $P (x, y)$ is equidistant from the points $(3, 6)$ and $(-3, 4)$, obtain the relation between $x$ and $y$. Hence, find the coordinates of point $P$ if it lies on $x$-axis.
Show SolutionHide Solution↓
$\sqrt{(x - 3)^2 + (y - 6)^2} = \sqrt{(x + 3)^2 + (y - 4)^2}$ (1 Mark)
gives $-12x - 4y = -20$ or $3x + y = 5$ (1 Mark)
As P lies on $x$ axis so $y = 0$ gives $x = \frac{5}{3}$ (1/2 Mark)
Coordinates of P are $(\frac{5}{3},0)$ (1/2 Mark)
gives $-12x - 4y = -20$ or $3x + y = 5$ (1 Mark)
As P lies on $x$ axis so $y = 0$ gives $x = \frac{5}{3}$ (1/2 Mark)
Coordinates of P are $(\frac{5}{3},0)$ (1/2 Mark)