using a circle and its tangent to find a point

Question

The line L is a tangent to the circle x² + y² =98 at the point (-7,-7).

 

Line L crosses the x axis at point P. 

 

work rn out the coordinates of point p 

Answer 1

The tangent line is perpendicular to the radius at the point (-7, -7).

The slope of the radius at the point (-7, -7) is 1.

The slope of the tangent line is -1

y = ms + b

-7 = (-1)(-7) + b

-7 = 7 + b

-14 = b

 

The tangent has an x-intercept of -14.