Question

The two conics bx2 = y and $\frac{x^{2}}{a^{2}}–\frac{y^{2}}{b^{2}}$ = 1 intersect iff-

• A. $–\frac{1}{\sqrt{2}}$£ a £$\frac{1}{\sqrt{2}}$
• B. a < – $\frac{1}{\sqrt{2}}$
• C. a>$\frac{1}{\sqrt{2}}$
• D. a < b

Answer 1

Answer: (A)

$–\frac{1}{\sqrt{2}}$£ a £$\frac{1}{\sqrt{2}}$

Answer 2

Substituting x2 = $\frac{1}{b}$ y, the equation of the conic gives the equation a2y2 – by + a2b2 = 0. This has real roots iff

b2 – 4a4b2 ³ 0 i.e., a4 £ $\frac{1}{4}$ giving $–\frac{1}{\sqrt{2}}$ £ a £ $\frac{1}{\sqrt{2}}$