conic sections

[roadrunner]

I need assistance with the following two problems:

Find an equation for each parabola satisfying the following conditions:

a) Axis of symmetry parallel to the x axis, contains the points (0,1), (3,2), (1,3).

b) Contains the points (1,10) and (2,4), axis of symmetry is vertical, vertex is on the line 4x-3y = 6.

For (a) I plugged the points into the equation for a horizontal parabola, etc., but cannot continue with the equations.

For (b) I tried something similar while also using the equation of the line.

Any help will be appreciated.

Thanks in advance.

 

[stapel]

a) "Parallel to the x-axis" means "of the form x = ay² + by + c". Now plug in the three given (x, y) points, getting a system of three equations in three unknowns (being "a", "b", and "c"). For instance, the second point gives you the equation "3 = 4a + 2b + c".

Solve the system.

(What you've posted implies you've made progress along these lines, but you haven't shown what you've done, so it is difficult to provide specific assistance.)

b) "Axis of symmetry is verticle" means "of the form y = ax² + bx + c". How are you using the line equation (y = (4/3)x - 2) at this point?

Thank you.

Eliz.