Question

How many points are 4 units from the origin and 2 units from the linbe x=-1?

Answer 1

There are two points, 4 units from the origin and 2 units from the line x = -1.

What are coordinates?

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;

brainly.com/question/27749090

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