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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

01

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.

02

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 isr=(1-4)2+(-2-(-2))22=(-3)2+0=3

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.

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

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