Question

find the equation of locus of a point such that the difference of the squares of its distance from the points (5,0) and (2,3) is 10​

Answer 1

Step-by-step explanation:

let us consider the point p be the point on the locus p (x , y)

As we have given condition,

the difference of the squares of its distance from the points (5,0) and (2,3) is 10

let us consider the points are,

A (5,0)

B (2,3)

therefor,

AP² - BP² = 10

(0-y)² + (5-x)² - ((3-y)² + (2-x)²)

= 10

y² + 25 - 10x + x²

- ((9 - 6y + y²) + (4 - 4x + x²) = 10

y² + 25 -10x + x²

-9 + 6y - y² -4 + 4x - x² = 10

25 -9 - 4 - 10x + 4x + x² + 6y = 10

25 - 13 - 6x + x² + 6y = 10

12 - 10 - 6x + x² + 6y = 0

x² - 6x + 6y + 2 = 0

therefor x² - 6x + 6y + 2 = 0 is required equation of the locus .