the set of points in a plane such that the difference of the distances from (2,5) and (2,-5) is 8

Question

Find the equation using the distance formula

Answer 1

you can use

sqrt((x-2)^2 + (y-5)^2) - sqrt((x-2)^2 + (y+5)^2)) = 8

this is a tedious process but eventually you can get an equation of hyperbola

the focus is at (2,5) and (2,-5)

c = 5, a = 4, b = 3 and the equation is

y^2/a^2 - (x-2)^2/b^2 = 1

Answer 2

Isosceles triangle. One side is 10 units. The other 2 sides is 8 units.

Try using the distance formula.

d^2 = (x- x1)^2 + (y-y1)^2