Question
Question: The locus of the point of intersection of the tangents to the parabola x<sup>2</sup> – 4x – 8y + 28 ...
The locus of the point of intersection of the tangents to the parabola x2 – 4x – 8y + 28 = 0 which are at right angle is –
A
y = 0
B
y = – 1
C
x = 1
D
y = 1
Answer
y = 1
Explanation
Solution
x2 – 4x – 8y + 28 = 0
locus of pt of intersection of ^ tangents is directrix
x2 – 4x + 4 = 8y – 28 + 4 ̃ (x – 2)2 = 8y – 24
(x – 2)2 = 8(y – 3) ̃ X2 = 8Y
equation of directrix
Y = – 2 ̃ y – 3 = – 2 ̃ y = 1