Question

The equation of the locus of the point whose

distance from y-axis is half the distance from

origin is

(1) x2

+ 3y2

= 0 (2) x2

- 3y2

= 0

(3) 3x2

+ y2

= 0 (4) 3x2

- y

2

= 0​

Answer 1

To find -

Find the equation of the locus of the point whose distance from y-axis is half the distance from origin .

Solution -

Let us assume that , such a point R exists with the coordinates

( h, k ) .

Now , the distance of the point from the y axis is half the distance

from the origin .

Coordinates of that point on the Y axis -

=> [ 0, k ] .

Here ,

PR = ½ PQ

=> 2PR = PQ

=> 4 [ PR ]² = [ PQ ]² .

=> 4 h² = h² + k²

=> 3h² = x² .

Replacing the coordinates by x and y -

=> 3x² = y²

=> 3x² - y² = 0 .

Thus , Option 2 is the correct answer.

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