Question

The number of values of `c` such that the straight line `y=4x+c` touches the curve `(x^2)/4+(y^2)/1=1` is 0 (b) 1 (c) 2 (d) infinite

Answer 1

Correct Answer - B
for ellipse , condition of tangency is `c^(2)= a^(2) m^(2) +b^(2)`
given line is y= 4x+ c and curve `(x^(2))/(4)+y^(2)=1`
`implies c^(2) = 4xx4^(2)+1=65`
`implies c=+- sqrt(64)`
so , there are two different values of C.