I will give brainliest The equation of a parabola is given.y=14x2−3x+18What are the coordinates of the focus of the parabola?Enter your answer in the boxes.

Solution:The equation of a parabola is given as [tex] y=14x^2-3x+18 [/tex]we have been asked to find the coordinates of the focus of the parabola?The given equation can be re-written as [tex] 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})\\ [/tex]As we know in standard form of [tex] (x - h)^2 = 4p (y - k) [/tex], the focus is (h, k + p)So on comparision we get [tex] 4p=\frac{1}{14}\\ \\ P=\frac{1}{56}\\ [/tex][tex] Focus=(\frac{3}{28},\frac{999}{56}+\frac{1}{56} )\\ \\ Focus=(\frac{3}{28}, \frac{125}{7}) [/tex]