Question

Length of latus rectum of the parabola whose parametric equation is x = t² + t + 1, y = t² – t + 1 where tÎR, is equal to

• A. 8
• B. 4
• C. 2
• D. None

Answer 1

Answer: (D)

None

Answer 2

x = t² + t + 1

y = t² – t + 1

x – y = 2t

t = $\left( \frac{x - y}{2} \right)$

x = $\frac{(x - y)^{2}}{4} + \frac{x - y}{2} + 1$

(x – y)² = 2(2x – x + y – 2)

(x – y)² = 2(x + y – 2)

2$\left( \frac{x - y}{\sqrt{2}} \right)^{2} = \sqrt{2} \times 2\left( \frac{x + y - 2}{\sqrt{2}} \right)$

y² = 4ax

4a = $\sqrt{2}$