Question

If A and B are points on the parabola y² = 4ax with vertex O such that OA perpendicular to OB and having lengths r₁ and r₂ respectively, then the value of $\frac{{r_{1}}^{4/3}{r_{2}}^{4/3}}{{r_{1}}^{2/3} + {r_{2}}^{2/3}}$ is

• A. 16a²
• B. a²
• C. 4a
• D. None of these

Answer 1

Answer: (A)

16a²

Answer 2

Q r₁² sin²q = 4ar₁ cosq

r₁ = $\frac{a\cos\theta}{\sin^{2}\theta}$

r₂ = $\frac{a\sin\theta}{\cos^{2}\theta}$

put in $\frac{r_{1}^{4/3}r_{2}^{4/3}}{r_{1}^{2/3} + r_{2}^{2/3}}$