Question

The value(s) of $\left[c\right]$ for which the line $y=4x+c$ touches the curve $x^2+16y^2=16$ is/are (where $[.]$ represents greatest integer function)

• A. $-16$
• B. $-17$
• C. $16$
• D. $17$

Answer 1

Answer: (B), (C)

$16$

Given curve is ellipse with
$a^2=16,b^2=1$
and the slope of the line is $m=4$
Hence using the tangency condition
$c=\pm \sqrt{a^2{m}^2+b^2}\Rightarrow c=\pm \sqrt{16\cdot 16+1}=\pm \sqrt{257}\therefore \left[c\right]=-17,16$