There are two points, 4 units from the origin and 2 units from the line x = -1.
<h3>What are coordinates?</h3>
Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
Given point is at a distance of 4 units from origin,
that is √x² + y² = 4
x² + y²= 16 is the equation of the locus of the point.
The given point is also 2 units from the line x =-1
that is √(x+1)² + y² = 2
(x+1)² + y²= 4 is the equation of the locus of the point.
Subtracting the second given equation from the first one,
we get x² - (x+1)² = 12
simplifying, x = 11/2
So the common coordinate point for these 2 points which is 11/2.
Substituting this value to the first equation,
(11/2)²+ y² = 16
Simplifying, y = ±(i√57)/2.
There are 2 points whose coordinates are;
( i√57/2 , 11/2 ) and ( -i√57/2 , 11/2 ).
Therefore there are two points, 4 units from the origin and 2 units from the line x = -1.
To learn more about the coordinates;
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