Question

The tangent at the point A(12, 6) to a parabola intersects its directrix at the point B(–1, 2). The focus of the parabola lies on x-axis. The number of such parabolas is-

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (D)

4

Answer 2

Let the focus be S(a, 0)

Since AS and BS are perpendicular to each other

̃ . $\frac { 2 } { - ( 1 + a ) }$= –1 ̃ a = 0, 11

̃ the focus is (0, 0) or (11, 0).The slope of the directrix be m. Also, distance of S from the line (y –2) = m(x + 1) is same as AS

̃ (m (13 – 6))² = (1+ m²) (180) or (m(13) – 6)²

= (1 + m²) (37)

̃ 4 values of m are possible. Hence there are four parabolas.