Question

Find the locus of the point whose distance from the point (0,4) is 2/3 of its distance from the line y=9

Answer 1

Given:

Locus is at a distance from the point (0,4) is 2/3 of its distance from the line y=9.

To find:

Find the locus of the point.

Solution:

From given, we have the data as follows.

Locus is at a distance from the point (0,4) is 2/3 of its distance from the line y = 9.

[√{(h - 0)² + (k - 4)²}]² = (2/3 |(k - 9)/√1²|)²

taking root on both the sides, we get,

h² + (k - 4)² = 4/9 ( (k - 9)²/1 )

9h² = 9 (k - 4)² = 4 (k - 9)²

9h² + 9k² + 144 - 72k = 4k² + 324 - 72k

9h² + 9k² - 4k² - 324 + 144 = 0

9h² + 5k² = 180

9h²/180 + 5k²/180 = 1

h²/20 + k²/36 = 1

replace (h, k ) by (x, y)

x²/20 + y²/36 = 1