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Chapter 1: Q.41 (page 50)

Find the standard form of the equation of each circle.

Center (-1, 3) and tangent to the line y = 2

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information

Given that the circle centered at(-1,3) and tangent to the line y=2

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

02

Step 2. Description of finding  radius r of the circle

Here circle center at (-1,3) and tangent to line y=2 means a line drawn from center to the point (-1,3), perpendicular to y=2, will intersect at (-1,2). Thus the distance from (-1,2) to (-1,3 ) is the radius and then the radius r=(-1-(-1)2+(2-3)2=0+1=1

03

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=r2.

Here radius r=1 then the equation of the given circle becomes(x-(-1))2+(y-3)2=12(x+1)2+(y-3)2=1

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Most popular questions from this chapter

True or False Two triangles are congruent if two angles and the included side of one equals two angles and the included side of the other.

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

(2,0);(2,2)

Find the distance d(P1,P2)between the points P1andP2.

P1=(-4,-3);P2=(6,2)

Find the midpoint of the line segment joining the points P1 and P2 .

P1=(-2,0);P2=(2,4)

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

(-2,3);(2,1)
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