Chapter 1: Q 35. (page 51)

The endpoints of the diameter of a circle are $(- 3, 2)$ and $(5, - 6)$ . Find the center and radius of the circle .Write the general equation of this circle.

Short Answer

Expert verified

Center and radius of circle are $(1, - 2)$ and $\sqrt{32}$ and general form of equation is $x^{2} + y^{2} - 2 x + 4 y = 27$ .

Step by step solution

Step 1. Given information.

Consider the given endpoints $(- 3, 2)$ and $(5, - 6)$ .

Step 2. Formula used for center and radius .x1+x22 ,y1+y22 and d=x2-x12+y2-y12

$(\frac{- 3 + 5}{2}, \frac{2 - 6}{2}) (1, - 2)$

Further simplify.

$d (O A) = \sqrt{{(1 + 3)}^{2} + {(- 2, - 2)}^{2}} d (O A) = \sqrt{32} d (O B) = \sqrt{{(1 - 5)}^{2} + {(- 2 + 6)}^{2}} d (O B = \sqrt{32})$

Further simplify.

Step 3. Using standard form of circle to find general form.x-h2+y-k2=r2

Substitute the value of $h, k, r$ .

${(x - 1)}^{2} + {(y + 2)}^{2} = {\sqrt{32}}^{2} x^{2} + y^{2} - 2 x + 4 y = 27$

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The endpoints of the diameter of a circle are $(- 3, 2)$ and $(5, - 6)$ . Find the center and radius of the circle .Write the general equation of this circle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Formula used for center and radius .x1+x22 ,y1+y22 and d=x2-x12+y2-y12

Step 3. Using standard form of circle to find general form.x-h2+y-k2=r2

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The endpoints of the diameter of a circle are -3,2and 5,-6. Find the center and radius of the circle .Write the general equation of this circle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Formula used for center and radius .x1+x22 ,y1+y22 and d=x2-x12+y2-y12

Step 3. Using standard form of circle to find general form.x-h2+y-k2=r2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

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Logic and Functions

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

The endpoints of the diameter of a circle are $(- 3, 2)$ and $(5, - 6)$ . Find the center and radius of the circle .Write the general equation of this circle.