A conic has equation $$ay^2+bx=0$$
where $a=5$ and $b=-315$. If the focus point is at $(F, 0)$ then what is the value of $F$ to 2 decimal places?
Hi, I want to check if i have applied the correct formula to solve this question. My answer is $F=15.75$.
This is my working:
$5y^2 - 315x =0$
$5y^2 = 315x$ (bringing $-315$ from LHS to RHS)
$y^2 = 315x$ divided by $5$
$y^2 = 63x$
$y^2 = 4ac$ (Equation of parabola in in standard position, where $a >0$)
$a = 63$ divided by $4$
$a = 15.75$
Your solution of $F=15.75$ is correct. Hence that if you are able to plug in the correct values in the right places, the equations came be solved by basic Algebra techniques you have learned. Which would solve for $F$.