Question

Find the equation of parabola whose vertex is (-5, -3) and ends of
latus rectum are (-1,5) and (-1 -11)​

Answer 1

Answer:

54..............................

Answer 2

Answer:

solution

Given vertex of parabola is (h,k) =(-5,-3)

so, h=-5 and k = -3

the two ends of latus ractum is (x1, y1) = (-1, 5) and (x2, y2) = ( -1, -11)

we know that,

The focus of the parabola is the middle point of latus ractum . so,

the focus is = (x1 + x2/2 , y1 +y2 / 2)

= ( -1-1 /2 , 5-11 /2 )

= ( -1 , - 3 )

or, (h+a, k ) = (-1 , -3 )

so, -5+a = -1

so, a = 4

since, the axis of parabola is parallel to x- axis . so, the eqn. of parabola is

(y-k)^2 = 4a (x-h)

( y+3)^2 = 16(x+5)

which is the required eqn of parabola . Ans