Answer:
y = - [tex]\frac{8}{15}[/tex] x + [tex]\frac{289}{15}[/tex]
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 = [tex]\frac{15-0}{8-0}[/tex] = [tex]\frac{15}{8}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{15}{8} }[/tex] = - [tex]\frac{8}{15}[/tex], thus
y = - [tex]\frac{8}{15}[/tex] x + b ← is the partial equation
To find b substitute (8, 15) into the partial equation
15 = - [tex]\frac{64}{15}[/tex] + b ⇒ b = 15 + [tex]\frac{64}{15}[/tex] = [tex]\frac{289}{15}[/tex]
y = - [tex]\frac{8}{15}[/tex] x + [tex]\frac{289}{15}[/tex] ← equation of tangent
