Question

How do you find an equation for the line tangent to the circle x2+y2=25 at the point (3, -4)?

Answer 1

Alright, lets get started.

The curve circle is given as
`x^(2) +y^(2) = 25`

We could find the slope by diffentiating it.

`(d)/(dx)(x^(2) +y^(2)) = (d)/(dx) 25`

`2x + 2y (dy)/(dx) = 0`

`x + y (dy)/(dx) = 0`

`(dy)/(dx) = -(x)/(y)`

We hve given the point (3,-4). Putting its value as (x,y)

`(dy)/(dx) = -(3)/(-4) = (3)/(4)` = m

The equation of line is y = mx + c

`-4 = (3)/(4)* 3 + c`

`-4 = (9)/(4) + c`

`c = -(9)/(4) - 4 = -(25)/(4)`

Putting the value of m and c in equation, Hence the eqution will be

`y = (3)/(4)x +(-(25)/(4) )`

Multiplying the complete equation with 4

`4y = 3x - 25`

or

`y = (3)/(4) x - (25)/(4)`

`3x - 4y - 25 = 0` : Answer

Hope it will help :)