Question

Find the equation of the parabola having (4, -8) as one of extremities of porabola​

Answer 1

Answer:

Equation of L.R. is

x=7,

Also focus is mid - point of L.R. is (7,4).

∴ Equation of axis is y−4=0(x−7,),m=0 as it is

⊥ to L.R. ∴y=4 is the equation of axis and

length of L.R. =2=4a,∴a=

2

1

Hence its vertex is at a distance a=

2

1

from focus S

on the axis y=4.

∴ Vertex is (7±

2

1

,4) or (7

2

1

,4) and (6

2

1

,4)

Hence its equation is Y

2

=4AX or Y

2

=−4AX

where Y=y−4,X=x−6.5 or x−7.5 and 4A=2

(y−4)

2

=2(x−6.5) or (y−4)

2

=−2(x−7.5)