A point moves in a manner that the sum of the squares of its distance from thr origin and the point (2,-3) is always 19.show that the locus of moving point is a circle.find the equation to the circle?
1 Answer
Explanation:
.
Let's create a figure we can use to solve this problem:
Point
We can use the distance formula to calculate the lengths of
Now, we add
Let's divide the entire equation by
We can rewrite this equation by adding and subtracting constants and grouping the
This is the equation of a circle in the form of:
where
Our equation is that of a circle, which is the locus of point