equation of the tangent

[maeveoneill]

a tangent to the parabola y=3x^2 -7x +5 is perpendicular to x+5y -10 =0. determine the equation of the tangent.
can someone explain how to do this. thanks. listen to some jack johnson.

 

[stapel]

a) Solve the equation "x + 5y - 10 = 0" for "y=". Read off the slope.

b) Find the perpendicular slope.

c) Differentiate the equation "y = 3x² - 7x + 5" to find the equation of the slope. Set the slope equation equal to the perpedicular slope you're needing. Solve for the x-value.

d) Plug this x-value into the parabola's equation to find the y-value for the point.

e) Take the slope from (b) above and the point from (d) above, and find the equation of the straight line through this point having this slope.

Eliz.