math
posted by EYOB .
if the line y=2x+b and the parabola y^2=8(x+2) meet exactly at one point,then what is the value of b

NonCalculus way:
Let's find their intersection, ...
(2x+b)^2 = 8(x+2)
4x^2 + 4bx + b^2  8x  16 = 0
4x^2 + (4b8)x + b^2  16 = 0
this is a quadratic with
A = 4
B = 4b 8
C = b^2  16
IF this is to have only one root, then the B^2  4AC, or the discriminant, must be zero.
so
(4b8)^2  4(4)(b^2  16) = 0
16b^2  64b + 64  16b^2 + 256 = 0
64b = 320
b =5
Using Calculus:
for y^2= 8x + 16
2y(dy/dx) = 8
dy/dx = 8/2y > slope of the tangent
but we know the slope of the tangent is 2 from y  2x+b
then 8/2y = 2
4y = 8, then y = 2
sub that into parabola
4 = 8x + 16
x = 12/8 = 3/2
so the point of contact is ( 3/2,2) which must satisfy
y = 2x + b
2 = 2(3/2) + b
2 = 3 + b
b = 5 , just like before.
Respond to this Question
Similar Questions

math
A parabola has the equation y = 4(x3)^27 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the yaxis D) The parabola does not cross the xaxis E) The … 
math
A parabola has the equation y = 4(x3)^27 Choose 2 true statements: A) The parabola has a minimum value B) The parabola has a maximum value C) The parabola does not cross the yaxis D) The parabola does not cross the xaxis E) The … 
MATH
True or False? 1.) A segment has exactly one perpendicular bisector. 2.) A line has exactly one perpendicular bisector. 3.)Given a line and a point not on the line, there is exactly one line perpendicular to the original line that 
maths
consider the line y=6xk and the parabola y=x^2 i) for what value of k is the line y=6xk a tangent to the parabola y=x^2 ? 
math
The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)9 at point P and the parabola y=4x^(2)+4x+5 at point Q. a. If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point Q, find the … 
calculus
The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)9 at point P and the parabola y=4x^(2)+4x+5 at point Q. a. If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point Q, find the … 
math
I need help with parametric equations, locus problems, tell me how to solve all questions if you can. Need help with one below: Tangents are drawn to a parabola x^2=4y from an external point A(x1,y1) touching the parabola at P and … 
precalculus
graph the parabola y=2x^26x3. plot point on the parabola A[1,7] and draw a line through A with an angle of inclination equal to 30 degrees. then find the equation of the line and its second point of intersection B, with the parabola 
Math
If f(x)=3x^25x, find the f'(2) & use it to find an equation of tangent line to the parabola y=3x^25x at the point (2,2). My ans is f'(2)=7 & y=7x12. What is parabola exactly? 
Math
A quadratic function is defined by f(x)=3.7x^2+6.8x+4.2. A linear function is defined by g(x)=0.5x+k. Determine the value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth