pre calc
posted by gabs .
Find the values of b such that the system has one solution.
x^2 + y^2 = 36
y= x+b
and then they give me an answer box
b=_________ (smaller value)
b=_________ (larger value)
i have absolutely no idea how to even begin this and what they are asking. could some please help and explain what im supposed to do with this. thanks so much!!!

sub in the straight line into the circle
x^2 + (x+b)^2 = 36
x^2 + x^2 + 2bx + b^2  36 = 0
for one solution the discriminant, that is
b^2  4ac = 0
(2b)^2  4(2)(b^236) = 0
4b^2  8b^2 + 288=
4b^2 = 288
b^2 = 72
b = ± √72 or ± 6√2 
Draw two tangents to the circle x^2+y^2=6^2 parallel to the line y=x in the second and fourth quadrants.
b is yintercept of these tangents.
Сonsider the algebraic method.
Find the coordinates of common points of the line and circle:
x^2+(x+b)^2=36
2x^2+2bx+b^236=0
Since the line is tangent then the equation has unique solution =>
the discriminant (2b)^24*2(b^236)=0
4b^28b^2+288=0
b^2=72
b=6sqrt(2) or b=6sqrt(2) 
Consider the geometric method.
b(b>0) is the leg in a isosceles rectangular triangle with height=6
6^2+6^2=b^2
Respond to this Question
Similar Questions

math214
Complete the following: (a) 1400 ft2 = _________ yd2 (b) 1/9 yd3 = _________ ft3 (c) 4.5 lb = _________ oz (d) 32 °C = _________ °F 
calc
Consider the function below. (Round the answers to three decimal places. If you need to use  or , enter INFINITY or INFINITY.) f(x) = 4 + 4x2  x4 (a) Find the intervals of increase. (Enter the interval that contains smaller numbers … 
CHEMISTRY (WEBWORK)
SPARTAN: Enter the numerical energy values (X, Y, & Z) on the yaxis and calculate the Ea and G. (Note: This is a multipart problem. First input your values for X, Y, and Z. When you are satisfied with your values submit them and check … 
physics
A person pulls with a force of 40 N on two boxes at rest. The top box is 3.0 kg and the bottom box is 6.0 kg. The coefficient of kinetic friction between the floor and the larger box is .20 and the angle is 30 degrees. a) if the smaller … 
physics
A person pulls with a force of 40 N on two boxes at rest. The top box is 3.0 kg and the bottom box is 6.0 kg. The coefficient of kinetic friction between the floor and the larger box is .20 and the angle is 30 degrees. a) if the smaller … 
calc
analyze the function ln x = cx^2 to find the unique value of c such that there is exactly one solution to the equation. to do this, find the value of c such that both sides of the equation have equivalent slopes at some point; this … 
Calculus
Consider the function f(x)=6xcos(x)+5 on the interval 0 is less than or equal to x, and x is less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k? 
Chemistry
What is the pH of the solution created by combining 12.30 mL of the 0.10 M NaOH(aq) with 8.00 mL of the 0.10 M HCl(aq)? 
Chemistry
What is the pH of the solution created by combining 12.30 mL of the 0.10 M NaOH(aq) with 8.00 mL of the 0.10 M HCl(aq)? 
alg.
Solve. (If there is no solution, enter NO SOLUTION.) y= x^2x4 y=x+4 (x, y) = ( , ) (smaller xvalue) (x, y) = ( , ) (larger xvalue) x^2 + y^2 =10 x+y=4 (x,y)= ( , ) smaller value (x,y)= ( , ) larger value