Question

We wants ul a point on the parabola y- = 18x where the ordinate is equal to three times the abscissa. Find the equation of the parabola whose focus is (2,5) and directrix is 3x + 4y + 1 = 0.​

Answer 1

Answer:

Let us assume that point P has abscissa a. Hence, the ordinate of point P is 3a.

Now, as P lies on y

2

=18x, substitute P in the equation of the parabola to find the value of a.

⟹(3a)

2

=18a

⟹9a

2

=18a

⟹a

2

=2a

⟹a=2 or a=0

If a=0 then, the abscissa and ordinate of P become the same and hence cannot be true according to given condition.

Hence, a=2 and the coordinates of required point are (2,6).