Question

I will give brainliest

Answer 1

Solution:

The equation of a parabola is given as

$y=14x^2-3x+18$

we have been asked to find the coordinates of the focus of the parabola?

The given equation can be re-written as

$y-18=14x^2-3x\\ \\ y-18=14(x^2-\frac{3}{14}x) \\ \\ y-18=14(x-\frac{3}{28})^2 -\frac{9}{56}\\ \\ y-18+\frac{9}{56}=14(x-\frac{3}{28})^2\\ \\ y-\frac{999}{56}= 14(x-\frac{3}{28})^2\\ \\ (x-\frac{3}{28})^2=\frac{1}{14}(y-\frac{999}{56})$

As we know in standard form of $(x - h)^2 = 4p (y - k)$, the focus is (h, k + p)

So on comparision we get

$4p=\frac{1}{14}\\ \\ P=\frac{1}{56}$

$Focus=(\frac{3}{28},\frac{999}{56}+\frac{1}{56} )\\ \\ Focus=(\frac{3}{28}, \frac{125}{7})$

Answer 2

Answer:

The answer is (6, 10)

Also, you might want to make sure you include the division line in 1/4 because 1/4 and 14 result in very different answers, thus the insane answer that someone else gave you!