You really should graph this problem.
The line is tangent to
at
If you use those points to find values of k and if you graph this correctly, you will see the answer.
Hello,
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
Hello,
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.
EB