A parabola y2 = 32x is drawn. From its focus, a line of slope 1 is drawn. The equation of the line is

Question

A parabola y2 = 32x is drawn. From its focus, a line of slope 1 is drawn. The equation of the line is (A)  y = x + 8  (B)  y = x - 4  (C)  y=x  (D)  y = x - 8

Tardigrade Admin · Accepted Answer

The given parabola is y2 = 32 x ...(i) Focus = (8, 0); Slope = 1 ⇒ Equation of line passing through (8, 0) and having slope 1 is y - 0 = 1(x - 8) ⇒ y = x - 8

Q. A parabola $y^{2} = 32 x$ is drawn. From its focus, a line of slope $1$ is drawn. The equation of the line is

$y = x + 8$

$y = x - 4$

$y = x$

$y = x - 8$

The given parabola is $y^{2} = 32 x ... (i)$
Focus $= (8, 0)$ ; Slope $= 1$
$\Rightarrow$ Equation of line passing through $(8, 0)$ and
having slope $1$ is $y - 0 = 1 (x - 8)$
$\Rightarrow y = x - 8$

Q. A parabola y2=32x is drawn. From its focus, a line of slope 1 is drawn. The equation of the line is

y=x+8

y=x−4

y=x

y=x−8