Question

Find the equation of tangent to the parabola $y^2=4x+5$ which is parallel to the line $y=2x+7.$

• A. $y=2x+3$
• B. $y=-2x+3$
• C. $y=2x+4$
• D. $y=2x-3$

Answer 1

The correct option is A $y=2x+3$

Any line parallel to given line is $y=2x+\lambda .$ If it is a tangent to the
parabola then it will meet it in two coincident points. Eliminating $x,$

$y^2-5=4x=2.2x=2(y-\lambda )$
or $y^2-2y+2\lambda -5=0.$ Its roots are equal

$\therefore B^2-4AC=0$ gives $4-4(2\lambda -5)=0$
or $24=8\lambda \therefore \lambda =3.$

$\therefore y=2x+3$ is the required tangent.