Question
Question: Circle drawn having it’s diameter equal to focal distance of any point lying on the parabola x<sup>2...
Circle drawn having it’s diameter equal to focal distance of any point lying on the parabola x2 – 4x + 6y + 10 = 0, will touch a fixed line whose equation is –
A
y = 2
B
y = –1
C
x + y = 2
D
x – y = 2
Answer
y = –1
Explanation
Solution
x2 – 4x + 6y + 10 = 0 ̃ x2 – 4x + 4 = –6 – 6y
̃ (x – 2)2 = –6 (y + 1)
Circle drawn on focal distance as diameter always touches the tangent drawn to parabola at vertex. Thus, circle will touch the line y + 1 = 0.