You really should graph this problem.
The line is tangent to
If you use those points to find values of k and if you graph this correctly, you will see the answer.
thanks in advance for anyone who can help me.
this question relates to linear quadratic systems
the question is:
Generalize your results for a circle of radius r and the line y = x+k
I thought maybe to help, I would put the question before this one, which relates to this question.
It goes like this
consider the circle x^2 + y^2 = 25 and the line y = x +k, where k is any real number. Determine the values of k for which the line will intersect the circle in one, two, or no points. Repeat for the circle x^2 + y^2 = 49 and the line y = x+k.
I figured out how to do this by subbing, x+k into the other equation, and then using discriminants to find out the values of k that would work.
im confused on the generalization question though.
Again, thanks to anyone who can help me
the circle has the equation:
and the line has the equation: .
To calculate the intercepts you plug in the term of the line into the equation of the xircle:
. After a few steps you'll get:
. Solve for x. Use the formula to solve quadratic equations:
You get 2 intercepts if the discriminant is greater than zero:
You get 1 intercept if the discriminant equals zero:
You get no intercepts if the discriminant is negative:
Solve for k to answer the question.