Wednesday

September 3, 2014

September 3, 2014

Posted by **Joseph** on Tuesday, May 24, 2011 at 8:13pm.

if the line y=mx+b intersects y^2=4px in only one point, show that p=mb

- calculus -
**Reiny**, Tuesday, May 24, 2011 at 8:51pmsub the straight line into the parabola

(mx+b)^ = 4px

m^2x^2 + 2mbx + b^2 - 4px = 0

m^2x^2 + x(2mb-4p) + b^2 = 0

to have one solution, (one intersection point), the discriminant has to be zero

(2mb-4p)^2 - 4(m^2)(b^2) = 0

4 m^2b^2 - 16mbp + 16 p^2 - 4m^2b^2 = 0

16mbp - 16p^2 = 0

16p(mb - p) = 0

so p = 0 or p = mb , but if p=0 we couldn't have a parabola, so

p = mb

**Answer this Question**

**Related Questions**

COLLEGE ALGEBRA - Suppose that R is the set of real numbers. Let f: R--> R be...

ALGEBRA - Suppose that R is the set of real numbers. Let f: R--> R be defined...

ALGEBRA - Suppose that R is the set of real numbers. Let f: R--> R be defined...

ALGEBRA - Suppose that R is the set of real numbers. Let f: R--> R be defined...

Math (Pre Cal) - Hi, I am studying for a precalculus quiz and I do not ...

math - L is a straight line in x-y plane. its equation is in the form y-8=m(x-1...

Algebra - do the indicated operations and write with only positive exponents and...

can someone please help me? - simplify the following expressions involving ...

geometry - Joey plots a point P on the line AB, as shown. Which statement is ...

Alg2 - The tangent to a circle may be defined as the line that intersects the ...