Respuesta :
Answer:
The coordinates of the focus of the parabola is:
[tex]\text{Focus}=(\dfrac{3}{28},\dfrac{125}{7})=(0.10714,17.8571)[/tex]
Step-by-step explanation:
We know that for any general equation of the parabola of the type:
[tex](x-h)^2=4p(y-k)[/tex]
The focus of the parabola is given by:
Focus= (h,k+p)
Here we are given a equation of the parabola as:
[tex]y=14x^2-3x+18[/tex]
On changing the equation to general form as follows:
[tex]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})[/tex]
Hence, we have:
[tex]h=\dfrac{3}{28}\ ,\ k=\dfrac{999}{56}\ ,\ p=\dfrac{1}{56}[/tex]
Hence,
[tex]k+p=\dfrac{1000}{56}=\dfrac{125}{7}[/tex]
Hence, focus is:
[tex]\text{Focus}=(\dfrac{3}{28},\dfrac{125}{7})=(0.10714,17.8571)[/tex]
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!
