Question

The line L is a tangent to the circle x2 + y2 = 45 at the point (-3, 6).

Answer 1

Answer:

The point P is (-15,0).

Step-by-step explanation:

We need to find the slope of the line L to get the coordinates of P.

We know that L is tangent to the circle at point (-3, 6), which means L is perpendicular to the radius of the circle (a line between the origin (0,0) and the tangent point (-3,6))

So let's find the slope or the radius.

$m_{R}=\frac{6-0}{-3-0}$    

$m_{R}=-2$

Now, we know that if two lines are perpendiculars their slopes follow the rule:

$m_{L}=-\frac{1}{m_{R}}$  

$m_{L}=\frac{1}{2}$  

Knowing the slope of L we can find the equation of this line. The slope-intercept equation of a line is:

$y=mx+b$

$y=\frac{1}{2}x+b$

Using the point (-3,6) we can find b.

$6=\frac{1}{2}(-3)+b$

$b=\frac{15}{2}$

The line equation will be:

$y=\frac{1}{2}x+\frac{15}{2}$

The point P has only an x-coordinate value (x,0)

So we have:

$0=\frac{1}{2}x+\frac{15}{2}$

$x=-15$

Therefore, the point P is (-15,0).

I hope it helps you!