Question

The polar of a point P w.r.t. y² = 4ax touches the circle

x² + y² = 4a². Then the equation to the locus of P is

• A. x² - y² = a²
• B. x² - y² = 2a²
• C. x² - y² = 4a²
• D. x² + y² = 4a²

Answer 1

Answer: (C)

x² - y² = 4a²

Answer 2

The polar of P(x₁, y₁) w.r.to y² = 4ax is yy₁ = 2a(x+x₁)

⇒ 2ax – y₁y+2ax₁ = 0 is tangent to the circle x² + y² = 4a²

⇒ Perpendicular distance from centre to the polar = radius of the circle.

$\frac{|2ax_{1}|}{\sqrt{4a^{2} + {y_{1}}^{2}}} = 2a$ ⇒ locus of (x₁, yy₁) is x² – y² = 4a².