Question

If the line $3x-4y+5=0$ is a tangent to the parabola $y^2=4ax,$ then $a$ is equal to

• A. $\frac{15}{16}$
• B. $\frac{5}{4}$
• C. $-\frac{4}{3}$
• D. $-\frac{5}{4}$

Answer 1

Answer: (A)

The given line is $y=\frac{3}{4}x+\frac{5}{4}=mx+c$
where $m=\frac{3}{4},c$
$=\frac{5}{4}$
$y=mx+c$ touches $y^2=4ax$ if $c=\frac{a}{m}$
$\therefore$ the given line touches $y^2=4ax$
if $\frac{5}{4}=\frac{a}{3/4}$
$\Rightarrow a=\frac{5}{4}\times \frac{3}{4}$
$=\frac{15}{16}$