1.a. state the parabola y^2 - 8x - 4y + 44 = 0 in conical form b. Find the I. Focus II. Directrix III. The coordinates of the ends of the Latus rectum?
1 Answer
(a) Canonical form of equation of parabola is
(b) I. Focus is
Explanation:
Canonical form of equation of parabola is
In the equation
Points on the latus rectum are two times away from the focus than the distance of focus from vertex, but at right angles to the axis of symmetry.
The given equation is
or
or
Hence, we have
I. Focus is
II. Directrix is
III. Coordinates of end points of latus rectum are
graph{(y^2-8x-4y+44)(x-3)((x-7)^2+(y-2)^2-0.03)((x-7)^2+(y-6)^2-0.03)((x-7)^2+(y+2)^2-0.03)(y-2)(x-7)=0 [-1.29, 18.71, -3.08, 6.92]}