Question

How to do this help please

Answer 1

Answer:

y = - $\frac{8}{15}$ x + $\frac{289}{15}$

Step-by-step 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 = $\frac{15-0}{8-0}$ = $\frac{15}{8}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{15}{8} }$ = - $\frac{8}{15}$, thus

y = - $\frac{8}{15}$ x + b ← is the partial equation

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

15 = - $\frac{64}{15}$ + b ⇒ b = 15 + $\frac{64}{15}$ = $\frac{289}{15}$

y = - $\frac{8}{15}$  x + $\frac{289}{15}$ ← equation of tangent