Chapter 1: Q.40 (page 50)

Find the standard form of the equation of each circle.
Circle with endpoints of a diameter at (4,3) and (0,1)

Short Answer

Expert verified

The standard form of the equation of a circle with endpoints of a diameter at (4,3) and (0, 1) is ${(x - 2)}^{2} + {(y - 2)}^{2} = 5$

Step by step solution

Step 1. Given information

Here given that circle with endpoints of a diameter at (4,3) and (0,1).

We need to find the standard form of the equation of a circle.

Step 2. Explanation about finding radius r of the circle

According to the question circle endpoint with a diameter is

(4,3) and (0,1) . The center of the circle is the midpoints of the circle endpoints (4,3) and (0,1) , hence the center is $(\frac{4 + 0}{2}, \frac{3 + 1}{2}) = (2, 2), w e k n o w t h a t m i d p o i n t (x, y) i s b e t w e e n (x_{1}, y_{1}) a n d (x_{2}, y_{2}) a n d t h e n (x, y) = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ The radius is the distance between the endpoint to the center, thus radius r is

$r = \sqrt{{(4 - 2)}^{2} + {(3 - 2)}^{2}} = \sqrt{{(2)}^{2} + 1} = \sqrt{4 + 1} = \sqrt{5}$

Step 3. Formation of standard of the equation of the circle

The standard form of the equation of a circle is of radius r with center at the

origin (h, k) is ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$

Thus the equation of the given circle is ${(x - 2)}^{2} + {(y - 2)}^{2} = {\sqrt{5}}^{2} {(x - 2)}^{2} + {(y - 2)}^{2} = 5$

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Find the standard form of the equation of each circle.
Circle with endpoints of a diameter at (4,3) and (0,1)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation about finding radius r of the circle

Step 3. Formation of standard of the equation of the circle

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Find the standard form of the equation of each circle.Circle with endpoints of a diameter at (4,3) and (0,1)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation about finding radius r of the circle

Step 3. Formation of standard of the equation of the circle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Find the standard form of the equation of each circle.
Circle with endpoints of a diameter at (4,3) and (0,1)