The coordinates of three points O,A,B are (0,0), (0,4), (6 0) respectively A point P moves so that the - Maths - Straight Lines

Question

The coordinates of three points O,A,B are (0,0), (0,4), (6 0)
respectively A point P moves so that the area of the triangle POA
is twice the area of the traingle POB Find the equation to both
parts of the locus of P

Aakash Sharma · Accepted Answer

The three given points are origin, one on x -axis and other on y - axis.

Let the coordinates of P be (x, y)

we know that area of triangle = $\frac{1}{2} \times base×height$

Now Δ POA = Δ POB

$∴ \frac{1}{2} \cdot 4 x = \pm 2 \cdot \frac{1}{2} \cdot 6 y$

⇒ 2x = ± 6y

⇒ x = ± 3y

Hence the required locus of both parts is (x – 3y) (x + 3y) = 0

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The coordinates of three points O,A,B are (0,0), (0,4), (6.0) respectively. A point P moves so that the area of the triangle POA is twice the area of the traingle POB. Find the equation to both parts of the locus of P.