Question

The common tangents to the circle x² + y² = a²/2 and the parabola y² = 4ax intersect at the focus of the parabola-

• A. x² = 4ay
• B. x² = –4ay
• C. y² = –4ax
• D. y² = 4a(x + a)

Answer 1

Answer: (C)

y² = –4ax

Answer 2

Equation of a tangent to the parabola y² = 4ax is

y = mx + a/m.

$\frac{a}{m} = \left( \frac{a}{\sqrt{2}} \right)\sqrt{1 + m^{2}}$Ž 2 = m² (1 + m²)

Ž m⁴ + m² – 2 = 0 Ž (m² – 1) (m² + 2) = 0

Ž m² = 1 Ž x = ± 1

Hence the common tangents are y = x + a and y = –x –a which intersect at the point

(–a, 0) which is the focus of the parabola y² = –4ax.