CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let $$x + y = k$$ be a normal to the parabola $$y^{2} = 12x$$. If p is the length of the perpendicular from the focus of the parabola onto this normal, then $$4k - 2p^{2} =$$


A
1
loader
B
0
loader
C
1
loader
D
2
loader

Solution

The correct option is D $$0$$
$$y^{2} = 12x$$ has normal $$x + y = k$$
$$y = tx + 2at + at^{3}$$
Here, $$a = 3$$
$$y = -tx + 6t + 3t^{3}$$ comparing
$$\Rightarrow y = k - x$$
So, $$t = 1$$
$$\Rightarrow k= 6t + 3t^{3} = 9$$
distance of focus from normal,
$$P = \dfrac {|3(1) - 9|}{\sqrt {2}} = \dfrac {6}{\sqrt {2}}$$
So, $$4k -2p^{2} = 36 - 2\left (\dfrac {36}{2}\right ) = 0$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image