Geometry Question- homework help
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Dr.Peterson
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I can't tell what methods or formulas you might have learned (I should say, that your class has been taught), so I don't know how to help.
But it looks like you are likely expected to plot the circle using its center and radius, read from the equation; then likely use the fact that a tangent is perpendicular to the radius at the point of tangency to find the slope of the line. Then, knowing the slope and the point, you can write the equation.
Please do whatever you are able to do, and tell us where you need help and why. If you can show us what was taught that you missed, we can help you understand it.
AmandasMathHelp
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Drawing the picture will for sure help. Draw the circle (you can get its radius and center from the equation- let us know if you need help with that).
Then draw a line from the center of the circle to that point on it (-4,2). You will need the slope of this line to figure out the slope of the tangent line.
The "tangent line" just touches the circle at that one point (-4,2). Picture like putting a stick on the side of the circle. As said above, this tangent line will actually be perpendicular (at a 90 degree angle to) the other line you drew from the center to the point. Hopefully you know how the slopes of perpendicular lines are related!!
Then draw a line from the center of the circle to that point on it (-4,2). You will need the slope of this line to figure out the slope of the tangent line.
The "tangent line" just touches the circle at that one point (-4,2). Picture like putting a stick on the side of the circle. As said above, this tangent line will actually be perpendicular (at a 90 degree angle to) the other line you drew from the center to the point. Hopefully you know how the slopes of perpendicular lines are related!!
HallsofIvy
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\(\displaystyle (x- 2)^2+ (y+ 6)^2= 100\) gives a circle with center at (2, -6) and radius 10. You can check that \(\displaystyle (-4- 2)^2+ (2+ 6)^2= 36+ 64= 100\) so, yes, (-4, 2) is on that circle. Further, the slope or the line segment (a radius) from (2, -6) to (-4, 2) is \(\displaystyle \frac{2- (-4)}{-6- 2}= \frac{6}{-8}= -\frac{3}{4}\). The tangent passes through (-4, 2) and is perpendicular to that radius so what is its slope?