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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.