Chapter 1: Q.35 (page 50)

Find the standard form of the equation of each circle.
Center at the origin and containing the point (-2, 3)

Short Answer

Expert verified

The standard form of the equation of a circle center at the origin and containing point (-2,3) is $x^{2} + y^{2} = 13$

Step by step solution

Step 1. Given information

Here is a circle with center at the origin and containing the point (-2,3) is given.

we have to form the standard form of the equation of a circle

Step 2. Find radius r of the circle

To find the equation of a circle we need to know the radius r. Since point (-2, 3) is given., the radius is equal to the distance from (-2, 3) to the center (0,0). So radius

$r = \sqrt{{(- 2 - 0)}^{2} + {(3 - 0)}^{2}} \sin c e d i s \tan c e b e t w e e n 2 p o i n t s f r o m (x_{1,} y_{1}) t o (x_{2,} y_{2}) i s \sqrt{{(x_{2 -} x_{1})}^{2} + {(y_{2 -} y_{1})}^{2}} = \sqrt{4 + 9} h e r e (x_{1,} y_{1}) i s (0, 0) a n d (x_{2,} y 2) i s (- 2, 3) . = \pm \sqrt{13} H e n c e r a d i u s i s \pm \sqrt{13 .}$

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

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

origin (0,0) is

$x^{2} + y^{2} = r^{2}$ .

Here radius r is $\sqrt{13}$ , thus the standard form of the equation of circle islocalid="1646842721588" $x^{2} + y^{2} = {(\sqrt{13})}^{2} x^{2} + y^{2} = 13$

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Find the standard form of the equation of each circle.
Center at the origin and containing the point (-2, 3)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find radius r of the circle

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

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Find the standard form of the equation of each circle.Center at the origin and containing the point (-2, 3)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find radius r of the circle

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Statistics

Mechanics Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Find the standard form of the equation of each circle.
Center at the origin and containing the point (-2, 3)