If three normals are drawn from the point (c , 0) to the parabola y2=4x and two of which are perpendicular, then the value of c is equal to

Question

If three normals are drawn from the point (c , 0) to the parabola y2=4x and two of which are perpendicular, then the value of c is equal to (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

Equation of the normal in slope form is y=mx-2m-m3 which passes through (c , 0) ⇒ 0=mc-2m-m3 ⇒ m3+(2 - c)m=0 ⇒ m=0 or m2+(2 - c)=0 ⇒ m1m2=(2 - c/1)=-1 ⇒ c=3

Q. If three normals are drawn from the point $(c, 0)$ to the parabola $y^{2} = 4 x$ and two of which are perpendicular, then the value of $c$ is equal to

$3$

$4$

$5$

$6$

Equation of the normal in slope form is $y = m x - 2 m - m^{3}$ which passes through $(c, 0)$
$\Rightarrow 0 = m c - 2 m - m^{3}$
$\Rightarrow m^{3} + (2 - c) m = 0$
$\Rightarrow m = 0$ or $m^{2} + (2 - c) = 0$
$\Rightarrow m_{1} m_{2} = \frac{2 - c}{1} = - 1$
$\Rightarrow c = 3$

Q. If three normals are drawn from the point (c,0) to the parabola y2=4x and two of which are perpendicular, then the value of c is equal to

3

4

5

6

Equation of the normal in slope form is y=mx−2m−m3 which passes through (c,0) ⇒0=mc−2m−m3 ⇒m3+(2−c)m=0 ⇒m=0 or m2+(2−c)=0 ⇒m1​m2​=12−c​=−1 ⇒c=3

Q. If three normals are drawn from the point $(c, 0)$ to the parabola $y^{2} = 4 x$ and two of which are perpendicular, then the value of $c$ is equal to

$3$

$4$

$5$

$6$

Equation of the normal in slope form is $y = m x - 2 m - m^{3}$ which passes through $(c, 0)$
$\Rightarrow 0 = m c - 2 m - m^{3}$
$\Rightarrow m^{3} + (2 - c) m = 0$
$\Rightarrow m = 0$ or $m^{2} + (2 - c) = 0$
$\Rightarrow m_{1} m_{2} = \frac{2 - c}{1} = - 1$
$\Rightarrow c = 3$