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

The Correct Option is 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}$