Question

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is ______.

विकल्प

• 3x² + 4y² = 192

• 4x² + 3y² = 192

• x² + y² = 192

• None of these

Answer 1

A point moves such that its distance from the point (4, 0) is half that of its distance from the line x = 16. The locus of the point is 3x² + 4y² = 192.

Explanation:

Let (h, k) be the coordinates of the moving point.

Then, we have

`sqrt((h - 4)^2 + k^2) = 1/2 (h - 16)/sqrt(1^2 + 0)`  (Why?)

(h – 4)² + k² = `1/4 (h - 16)^2`

4(h² – 8h + 16 + k²) = h² – 32h + 256

or 3h² + 4k² = 192

Hence, the required locus is given by 3x² + 4y² = 192