Chapter 1: Q.42 (page 50)

Find the standard form of the equation of each circle.
Center (4,-2) and tangent to the line x = 1

Short Answer

Expert verified

The standard form of the equation of a circle centered at(4,-2) and tangent to the line x=1 is ${(x + 1)}^{2} + {(y - 3)}^{2} = 1$

Step by step solution

Step 1. Given information

Given that the circle centered at(4,-2) and tangent to the line x=1

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

Step 2. Description of finding radius r of the circle

According to the given question circle center at (4,-2) and tangent to line x=1 means a line drawn from center to the point (4,-2), perpendicular to x=1, will intersect at (1,-2). Thus the distance from (1,-2) to center (4,-2 ) is the radius and then the radius is $r = {\sqrt{{(1 - 4)}^{2} + {(- 2 - (- 2))}^{2}}}^{2} = \sqrt{{(- 3)}^{2} + 0} = 3$

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 ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ .

Hence the equation of the given circle with a radius r is ${(x - 4)}^{2} + {(y + 2)}^{2} = 9$

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Find the standard form of the equation of each circle.
Center (4,-2) and tangent to the line x = 1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Description of 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.Center (4,-2) and tangent to the line x = 1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Description of 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

Decision Maths

Logic and Functions

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the standard form of the equation of each circle.
Center (4,-2) and tangent to the line x = 1