Question

The number of values of ‘c’ such that the straight line $y = 4x + c$touches the curve $\frac{x^{2}}{4} + y^{2} = 1$is

• A. 0
• B. 1
• C. 2
• D. Infinite

Answer 1

Answer: (C)

2

Answer 2

We know that the line $y = mx + c$touches the curve $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$iff $c^{2} = a^{2}m^{2} + b^{2}$

Here, $a^{2} = 4,b^{2} = 1,m = 4$∴$c^{2} = 64 + 1$⇒ $c = \pm \sqrt{65}$