Confused about a level 5 math question...?

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<p>So this is a grid-in response questions(It would help to draw it out):</p>

<p>Description of the figure:
There is a circle with a radius of 5(center at the origin), and each point on the circle satisfies the equation x^2+y^2=25. Then the problem states that line "l" is only tangent to the circle at point A. They say that point A is at (-4,y). No other intercepts or information is given. What is the slope of line "l"?</p>

<p>My approach:
I plug in -4 into the equation x^2+y^2=25 and solve for y.
I get y= 3. So point A is basically (-4,3)
I'm clueless what to do from there so I leave my answer as 3/4 since I know that slope =
(the change in y)/(the chance in x), but when I check my answer key, it says the answer is 4/3. Anyone care to explain where if I messed up or if I'm over-thinking this problem?
Thanks in advanced!</p>

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<p>The fundamental set up is correct (except for a negative error)</p>

<p>However, you overlooked the fact that when a line is tangent to a circle, the line drawn from the point of tangency to the center of the circle is perpendicular to said line. This is a often overlooked fact that shows up on both the SAT and ACT.</p>

<p>The slope of center of the circle to point A is actually -3/4. Therefore, line L has a slope of 4/3. (negative reciprocal)</p>

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<p>Oh man thanks! I can’t believe I overlooked that.</p>