The equation of the tangent to the parabola y2 = 8x which is parallel to the line 2x - y + 7 = 0, will be

Question

The equation of the tangent to the parabola y2 = 8x which is parallel to the line 2x - y + 7 = 0, will be (A) y = x + 1  (B) y = 2x + 1  (C) y = 3x + 1  (D) y = 4x + 1.

Tardigrade Admin · Accepted Answer

The equation of any tangent to the parabola y2 = 8x is y=mx+(2/m) which is parallel to 2x-y+7=0 whose slope m=2 On putting m=2 in (1), we get y=2x+1

Q. The equation of the tangent to the parabola $y^{2} = 8 x$ which is parallel to the line $2 x - y + 7 = 0,$ will be

$y = x + 1$

$y = 2 x + 1$

$y = 3 x + 1$

$y = 4 x + 1.$

The equation of any tangent to the parabola $y^{2} = 8 x$ is
$y = m x + \frac{2}{m}$
which is parallel to $2 x - y + 7 = 0$
whose slope $m = 2$
On putting $m = 2$ in $(1)$ , we get
$y = 2 x + 1$

Q. The equation of the tangent to the parabola y2=8x which is parallel to the line 2x−y+7=0, will be

y=x+1

y=2x+1

y=3x+1

y=4x+1.