Question

How to do this help please

Answer 1

y = -
`(8)/(15)` x +
`(289)/(15)`

Explanation:

The angle between the tangent and the radius at point P is 90°

Calculate the slope of the radius m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₂ - x₁ )

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (8, 15)

m =
`(15-0)/(8-0)` =
`(15)/(8)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((15)/(8) )` = -
`(8)/(15)`, thus

y = -
`(8)/(15)` x + b ← is the partial equation

To find b substitute (8, 15) into the partial equation

15 = -
`(64)/(15)` + b ⇒ b = 15 +
`(64)/(15)` =
`(289)/(15)`

y = -
`(8)/(15)` x +
`(289)/(15)` ← equation of tangent