Question -
Answer -
Given:
The focus S(2, 3) and directrix(M) x – 4y + 3 = 0.
Let us assume P(x, y) be any point on the parabola.
The distance between two points (x1, y1)and (x2, y2) is given as:
And the perpendicular distance from the point (x1,y1) to the line ax + by + c = 0 is
So by equating both, we get
Upon cross multiplication, we get
17x2 + 17y2 – 68x – 102y +221 = x2 + 16y2 + 6x – 24y – 8xy + 9
16x2 + y2 + 8xy – 74x – 78y+ 212 = 0
∴ The equation of the parabola is 16x2 + y2 +8xy – 74x – 78y + 212 = 0.
Now, let us find the length of the latus rectum,
We know that the length of the latus rectum is twice theperpendicular distance from the focus to the directrix.
So by using the formula,
∴ The length of the latus rectum is 14/√17