Question

How do you find the standard form of the equation of the parabola with a vertex of (1,0) and two points that are in the parabola are (5,3) and (5,-3)?

Answer 1

`4y^2=9(x-1)`.

Explanation:

As we look at the two given pts. `P(5,3) and Q(5,-3)` through which the reqd. Parabola passes, we immediately find that it is symmetric about X-axis.

So, its eqn. must be of the form `S : y^2=ax+b............(1)`

The pts. `P, Q and (1,0) all in S`

`:. 9=5a+b, 0=a+b rArr 9=4a rArr a=9/4, b=-9/4`

Hence, the Parabola `S : y^2=9/4(x-1), i.e., 4y^2=9(x-1)`.