+1993 The focus of a parabola is (−3,−4) . The directrix of the parabola is y=1 .
What is the equation of the parabola?
y=−1 /10 (x−3/2)^2+3
y=−1/20(x−3/2)^2−3
y=−1/20(x+3)^2+3/2
y=−1/10(x+3)^2−3/2
+128408 The directrix lies above the focus.....so...this parabola opens downward
To find the vertex ....we have ( -3, (-4 + 1)/2 ) = (-3, -3/2) = (h, k)
The distance from the vertex to the focus = p = l -4 - (-3/2) l = l -4 + 3/2l = l -8/2 + 3/2] = l -5/2l = 5/2
We have the following form
4p ( y - k) = - (x - h)^2 fill in what we know
4(5/2) (y - (-3/2) ) = - ( x - -3)^2 simplify
10 ( y + 3/2 ) = - ( x + 3)^2 divide both sides by 10
y + 3/2 = - (1/10) ( x + 3)^2 subtract 3/2 from both sides
y = - (1 /10) ( x + 3)^2 - 3/2
