Question

If the line 3x + ay – 20 = 0 cuts the circle x² + y² = 25 at real distinct or coincident points, then 'a' belongs to the interval –

• A. [–$\sqrt{7}$,$\sqrt{7}$]
• B. ($- \sqrt{7},\sqrt{7}$)
• C. (– , – $\sqrt{7}$] $\cup$ [ $\sqrt{7}$, )
• D. None of these

Answer 1

Answer: (C)

(– , – $\sqrt{7}$] $\cup$ [ $\sqrt{7}$, )

Answer 2

Centre (0, 0), r = 5

p £ r

Ž $\frac{20}{\sqrt{9 + a^{2}}}$< 5

4 £ $\sqrt{9 + a^{2}}$

Ž 9 +a² ³ 16

Ž a² ³ 7

Ž a² – 7  0

Ž (a – $\sqrt{7}$) (a + $\sqrt{7}$) ³ 0

a £ – $\sqrt{7}$ or a ³ $\sqrt{7}$