Question

Find the slope of a line passing through the following pair of point 

(²m²,2am) and (p²m²,2pm)

Answer 1

A(x₁,y₁) = A(a²m², 2am)

B(x₂, y₂) = B(p²m², 2pm)

Slope of line AB = `("y"_2 - "y"_1)/("x"_2 - "x"_1)``

                         = `(2"pm" - 2"am")/("p"^2"m"^2 - "a"^2"m"^2)`

                        = `(2"m" ("p" - "a"))/("m"^2("p"^2 - "a"^2)`

                       = `2/"m" xx ("p" - "a")/(("p" + "a")("p" - "a"))`

                       = `2/("m" ("p" + "a")`

                       = `2/("pm" + "am")`