Question

Помогите пожалуйста!!!Знайти параметр параболи y і рівняння її директриси, якщо відомо, що ця парабола проходить через точки перетинання прямої y=x з колом

Answer 1

Найдем точки пересечения 
$x^2+y^2-6x=0\\ y=x\\ \\ 2x^2-6x=0\\ x(2x-6)=0\\ x=0\\ x=3\\ y=0\\ y=3$
найдем p 
$3^2=6p\\ p=\frac{2}{3}$
директриса равна  x=$-\frac{\frac{2}{3}}{2}=-\frac{1}{3}$

Answer 2

Finding the Parameter of the Parabola and the Equation of Its Directrix

To find the parameter of the parabola and the equation of its directrix, we can use the given information that the parabola passes through the intersection points of the line y=x and the circle.

Parameter of the Parabola: The general equation of a parabola in vertex form is given by: \[ (x-h)^2 = 4p(y-k) \] where (h, k) is the vertex of the parabola and p is the parameter.

Equation of the Directrix: The equation of the directrix for a parabola in vertex form is given by: \[ y = k - p \]

Solution Steps:

1. Find the intersection points of the line y=x and the circle. 2. Use the intersection points to determine the parameter of the parabola. 3. Calculate the equation of the directrix using the vertex and the parameter.

Let's proceed with the solution steps to find the parameter of the parabola and the equation of its directrix.