Question

a circle with center c(4,-20 contains point d(8,1) what is the equation of a line perpendicular to the radius of a circle passing through point c

Answer 1

Explanation:

A circle with center c(4,-2) contains the point D( 8,1). What is the equation of the line perpendicular to the radius of the circle passing throug the point C

Answer 2

`y=-(4)/(21)x-(404)/(21)`

Explanation:

we know that

the segment CD is the radius of the circle

Step 1

Find the slope of the segment CD

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

`C(4,-20)\ D(8,1)`

Substitute the values

`m=(1+20)/(8-4)`

`m=(21)/(4)`

Step 2

Find the slope of the line perpendicular to the radius of the circle

we know that

If two lines are perpendicular. then the product of their slopes is equal to minus one

so

`m1*m2=-1`

we have

`m1=(21)/(4)`

substitute and solve for m2

`(21)/(4)*m2=-1`

`m2=-(4)/(21)`

Step 3

Find the equation of the line perpendicular to the radius of a circle passing through point c

we have

`m2=-(4)/(21)`

`C(4,-20)`

The equation of the line into point-slope form is equal to

`y-y1=m(x-x1)`

substitute the values

`y+20=-(4)/(21)(x-4)`

`y=-(4)/(21)x+(16)/(21)-20`

`y=-(4)/(21)x-(404)/(21)`