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Chapter 11: Q. 49 (page 1069)

Explain the relationship between the distance formula and the equation of a circle.

Short Answer

Expert verified

By using the distance formula, d=(x2-x1)2+(y2-y1)2, we can derive the equation of circle, that is, r2=(x-h)2+(y-k)2

Step by step solution

01

Step 1. To explain

To explain the relationship between the distance formula and the equation of a circle.

02

Step 2. Distance formula

The distance between any two points (x1,y1),(x2,y2) is d=(x2-x1)2+(y2-y1)2

03

Step 3. Consider a circle

Consider a circle in the rectangular coordinate system.
The radius is the distance from the center, (h,k)to a point on the circle, (x,y).

04

Step 4. To derive the equation of a circle,

Use the distance formula for the points (h,k),(x,y)for the distance r

d=(x2-x1)2+(y2-y1)2

05

Step 5. Substitute the values.

r=(x-h)2+(y-k)2

By squaring on both sides, we get,

r2=(x-h)2+(y-k)2

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