Question -
Answer -
Given:
Focus = (3, 3)
Directrix = 3x – 4y = 2
Firstly let us find the slope of the directrix.
The slope of the line ax + by + c = 0 is –a/b
So, m1 = -3/-4
= ¾
Let us assume the slope of axis is m2.
m1.m2 = -1
¾ . m2 = -1
m2 = -4/3
We know that the equation of the line passing through thepoint (x1, y1) and having slope m is (y – y1)= m(x – x1)
y – 3 = -4/3 (x – 3)
3(y – 3) = – 4(x – 3)
3y – 9 = – 4x + 12
4x + 3y = 21
On solving the lines, the intersection point is (18/5, 11/5)
By using the formula to find the length is given as
∴The length of the latus rectum is 2.