Question

The equation of a parabola is given.

Answer 1

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!

Answer 2

Answer:

The coordinates of the focus of the parabola is:

       $\text{Focus}=(\dfrac{3}{28},\dfrac{125}{7})=(0.10714,17.8571)$

Step-by-step explanation:

We know that for any general equation of the parabola of the type:

    $(x-h)^2=4p(y-k)$

The focus of the parabola is given by:

Focus= (h,k+p)

Here we are given a equation of the parabola as:

      $y=14x^2-3x+18$

On changing the equation to general form as follows:

$y=14(x^2-\dfrac{3}{14}x)+18\\\\\\y=14((x-\dfrac{3}{28})^2-(\dfrac{3}{28})^2)+18\\\\y=14(x-\dfrac{3}{28})^2-\dfrac{9}{56}+18\\\\\\y=14(x-\dfrac{3}{28})^2+\dfrac{999}{56}\\\\y-\dfrac{999}{56}=14(x-\dfrac{3}{28})^2\\\\(x-\dfrac{3}{28})^2=\dfrac{1}{14}(y-\dfrac{999}{56})\\\\(x-\dfrac{3}{28})^2=4\times \dfrac{1}{56}(y-\dfrac{999}{56})$

Hence, we have:

$h=\dfrac{3}{28}\ ,\ k=\dfrac{999}{56}\ ,\ p=\dfrac{1}{56}$

Hence,

$k+p=\dfrac{1000}{56}=\dfrac{125}{7}$

Hence, focus is:

$\text{Focus}=(\dfrac{3}{28},\dfrac{125}{7})=(0.10714,17.8571)$