+39 write the equation of the line tangent to the circle x^2 +y^2=169 at the point (-5,12)
+129840 write the equation of the line tangent to the circle x^2 +y^2=169 at the point (-5,12)
This is a circle of radius 13 that is centered at the origin
The slope of the line segment drawn from the circle's center to the point (-5/12) = the radius = -12/5
And since a tangent line to a circle at a given point is always perpendicular to the radius at that point, the slope of the tangent line = 5/12
And the equation of the tangent line is as follows:
y - 12= (5/12)(x - -5) simplify
y - 12 = (5/12)x + 25/12
y = (5/12)x + 169/12
Here's a graph : https://www.desmos.com/calculator/xefjptaopf
+118659 Find the gradient of the radius that touches the tangent.
The gradient of the tangent is the negative reciprocal.
Use the point and the gradient to determine the equation.
+129840 write the equation of the line tangent to the circle x^2 +y^2=169 at the point (-5,12)
This is a circle of radius 13 that is centered at the origin
The slope of the line segment drawn from the circle's center to the point (-5/12) = the radius = -12/5
And since a tangent line to a circle at a given point is always perpendicular to the radius at that point, the slope of the tangent line = 5/12
And the equation of the tangent line is as follows:
y - 12= (5/12)(x - -5) simplify
y - 12 = (5/12)x + 25/12
y = (5/12)x + 169/12
Here's a graph : https://www.desmos.com/calculator/xefjptaopf
+118659 max.Dave
What was wrong with my answer Max ?
Do you need to be spoon fed the answer? Is this so you can just copy it as your own work?
I gave you a good outline. If you needed the dots joined for you you could have just asked.
I am always prepared to give a great deal of my time to students who are actually trying to learn!
Thanks for the point recognition Michael :)
