question based on conic sections class 11

Question

a man visited india gate and moving on a path he observed that his distance from the gate is always 500 meters . taking india gate as origin answer the following questions

find the equation

if he saw a ballon seller is at a point 600,500 then the man moves towards gate or away from it

if man is considered to be at a point (400,300),then find the distance between man and ballon seller

Answer 1

find the equation: It sounds like this description is describing a circle with a radius of  500 meters.  So an equation representing this might be:  x² + y² = 500²

if he saw a ballon seller is at a point 600,500 then the man moves towards gate or away from it.  Sounds like the man is moving away from the gate. 

if man is considered to be at a point (400,300),then find the distance between man and ballon seller: distance between the man and the ballon seller is the square root of 200² + 200²  which turns out to be approximately 282.8 meters