Question

If the line $2x-3y=k$ touches the parabola $y^2=6x$, then the value of k is

• A. $-27/4$
• B. $-81/4$
• C. $-7$
• D. $27/4$

Answer 1

The correct option is A $-27/4$

$2x=k+3y$

Putting this in $y^2=6x$

$y^2=3(k+3y)\Rightarrow y^2-9y-3k=0$

For getting 1 value of $y$ as the line TOUCHES the parabola

We should put the Discriminant of the Quadratic Equation $D=0$

Hence, $9^2+12k=0\Rightarrow k=\frac{-81}{12}=\frac{-27}{4}$