Question

(Mathswatch)Can someone please help me with these questions. please I begg you! I BEGG YOU

Answer 1

Answer:

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

Step-by-step explanation:

First of all, the equation of the circle is

$x^{2} +y^{2} =17^{2}$

Where the radius is 17 units long.

Now, we need to find the slope of the radius OP,

$m=\frac{15}{8}$

Then, we use the perpendicular rule

$\frac{15}{8} \times m_{tangent}=-1\\ m_{tangent}=-\frac{8}{15}$

Next, we use the point-slope formula, with the slope we found and the point (8,15).

$y-y_{1} =m(x-x_{1} )\\y-15=-\frac{8}{15}(x-8) \\y=-\frac{8}{15}x+\frac{64}{15}+15\\ y=-\frac{8}{15}x+\frac{289}{15}$

Therefore, the equation of the tangent line is

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