Question

If $y=m x+c$ touches the parabola $y^2=4 a(x+a)$, then

(a) $c=\frac{a}{m}$

(b) $c=a m+\frac{a}{m}$

(c) $c=a+\frac{a}{m}$

(d) None of these

Answer 1

SOLUTION — Since, the line touches the parabola

$\begin{array}{l}\therefore \quad(m x+c)^2=4 a(x+a) \\\Rightarrow \quad m^2 x^2+(2 m c-4 a) x+c^2-4 a^2=0 \\\therefore \quad D=0 \Rightarrow(2 m c-4 a)^2=4 m^2\left(c^2-4 a^2\right) \\\Rightarrow \quad c=a m+\frac{a}{m} \\\end{array}$

So, The correct option of this question will be (B).