Identify the equation for the line tangent to the circle x2 + y2 = 100 at the point (−6, 8).

Answer 1

First, this circle has center at the origin with a radius of 10. Draw this picture.

Second, plot the point (-6,8) on the circle.

Third, draw a radius from the origin to this point. You should be able to determine the SLOPE of this radius. Since slope is -8/6, this reduces to -4/3.

Fourth, use the point-slope form to find the equation:

y - y₁ = m ( x - x₁)

y - 8 = -4/3 ( x - -6 )

y - 8 = -4/3 ( x + 6 ) This is the Point-Slope form of the equation.

Fifth, sometimes the question specifies the Slope-Intercept form of the equation. If that is the case, then you only have 2 steps left. First, distribute the -4/3 on the right side of the equation.

y - 8 = -4/3(x) + 8 Now, we isolate the "y" by adding 8 to both sides of the equation.

+8 +8

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y = -4/3(x) + 16