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Paragraph for comprehension 7 to 9

The tangents at P and P’ on the parabola y^2 = 4ax meet in T. S is the focus, O is the vertex and SP,
ST and SP’ are equal to , and respectively. The tangent at the point P(x1, y1) to the parabola
y2 = 4ax meets the parabola y^2 = 4a (x + b) at Q and R.

7. The normal chord at a point P on the parabola y^2 = 4ax subtends a right angle at vertex O. Then
the length of the chord is
(a) √3a
(b) 2√3a
(c) 4√3a
(d) 6√3a

8. The roots of the equation
αx^2 + 2βx + γ = 0 are
(a) Real and different
(b) Real and equal
(c) Complex numbers
(d) Irrational

9. If the chord of contact of tangents from point P to the parabola y^2 = 4ax touches the parabola
x^2 = 4by, the locus of P is
(a) circle
(b) parabola
(c) ellipse
(d) hyperbola