Alright, lets get started.
The curve circle is given as [tex] x^{2} +y^{2} = 25 [/tex]
We could find the slope by diffentiating it.
[tex] \frac{d}{dx}(x^{2} +y^{2}) = \frac{d}{dx} 25 [/tex]
[tex] 2x + 2y \frac{dy}{dx} = 0 [/tex]
[tex] x + y \frac{dy}{dx} = 0 [/tex]
[tex] \frac{dy}{dx} = -\frac{x}{y} [/tex]
We hve given the point (3,-4). Putting its value as (x,y)
[tex] \frac{dy}{dx} = -\frac{3}{-4} = \frac{3}{4} [/tex] = m
The equation of line is y = mx + c
[tex] -4 = \frac{3}{4}* 3 + c [/tex]
[tex] -4 = \frac{9}{4} + c [/tex]
[tex] c = -\frac{9}{4} - 4 = -\frac{25}{4} [/tex]
Putting the value of m and c in equation, Hence the eqution will be
[tex] y = \frac{3}{4}x +(-\frac{25}{4} ) [/tex]
Multiplying the complete equation with 4
[tex] 4y = 3x - 25 [/tex]
or
[tex] y = \frac{3}{4} x - \frac{25}{4} [/tex]
[tex] 3x - 4y - 25 = 0 [/tex] : Answer
Hope it will help :)
