Question

Find the equation of the tangent to $y=2x^2+7$ which is parallel to the line $4x-y+3=0$.

Answer 1

$y=2x^2+7$
$m_1=\frac{dy}{dx}=4x$
The slope of $4x-y+3=0$
$m_2=\frac{4}{1}=4$
$m_1=m_2\Rightarrow$Lines are parallel
$4x=4$
$x=1$
$y=2x^2+7=2(1{)}^2+7$
$y=9$
Equation of the tangent pt,(1,9) m=4
$y-y_1=m(x-x_1)$
$y-9=4x-4$
$4x-y+5=0$