Question

Two parabolas y2 = 4a (x –l1) and x2 = 4a (y – l2) always touch each other, l 1 and l 2 being variable parameters. Then, their points of contact lie on a

• A. Straight line
• B. Circle
• C. Parabola
• D. Hyperbola

Answer 1

Answer: (D)

Hyperbola

Answer 2

Let P1 : y2 = 4a (x –­ l1) and P2 : x2 = 4a (y – l2)

If both touch to each other than $\left( \frac{dy}{dx} \right)_{p_{1}}$ = $\left( \frac{dy}{dx} \right)_{p_{2}}$