Question

Help me please I beg

Answer 1

see explanation

Explanation:

(a)

calculate the gradient (slope) m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = O (0, 0 ) and (x₂, y₂ ) = A (- 5, 2 )

`m_(OA)` =
`(2-0)/(-5-0)` =
`(2)/(-5)` = -
`(2)/(5)`

(b)

the angle between a tangent and a radius at the point of contact is 90°

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(2)/(5) )` =
`(5)/(2)`

(c)

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m =
`(5)/(2)` , then

y =
`(5)/(2)` x + c ← is the partial equation

to find c substitute A (- 5, 2 ) into the partial equation

2 = -
`(25)/(2)` + c ⇒ c = 2 +
`(25)/(2)` =
`(29)/(2)`

y =
`(5)/(2)` x +
`(29)/(2)` ← equation of tangent