The line L is a tangent to the circle x2 + y2 = 45 at the point (-3, 6). The line L crosses the x-axis at the point P.
Work out the coordinates of P.

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.

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

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

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

The line equation will be:

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

So we have:

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

I hope it helps you!

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step-by-step explanation:

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