Question

A circle with center C (4,-2) contains the point D (8,1). what equation of the line perpendicular to the radius of the circle passing through point C?

Answer 1

`y`= -
`(4)/(3)`
`x`
`+`
`(10)/(3)`

Explanation:

Answer 2

First, determine the slope of the radius by the equation,

m = (y₂ - y₁)/ (x₂ - x₁)

Substituting the known values,
m = (1 - -2)/(8 - 4) = 3/4

If the unknown line is perpendicular to this, the slope should be the negative reciprocal which is equal to -4/3. Using the point-slope form to determine the equation,

y - y₁ = m(x - x₁)

Substituting the known values,

y - -2 = (-4/3)(x - 4)

Simplifying,
y + 2 = (-4/3)(x - 4)
3y + 6 = -4x + 16

Answer: 4x + 3y = 10