# The equation of a tangent to the parabola $\dpi{100} y^{2}=8x\; is\; y=x+2.$ The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is Option 1) (2, 4) Option 2) (–2, 0) Option 3) (–1, 1) Option 4) (0, 2)

S Sabhrant Ambastha

As we learnt in

Equation of tangent -

$y= mx+\frac{a}{m}$

- wherein

Tengent to $y^{2}=4ax$ is slope form.

$y^{2}=8x;$   Tangent is $y=x+2$

Slope of tangent, $m=1$

When two lines are perpendicular to each other,

$m_{1}\times 1=-1\:\:\:\Rightarrow m_{1}=-1$

Let the other tangent be $y=-x+c$

Now we have $y=mx+c$   touching $y^{2}=4ax$

$c=\frac{a}{m},\:\:\:\:a=2$

$c=-2$

$y=-x-2$

$y=x+2;\:\:y=-x-2$

So, $x+2=-x-2$

$x=-2$

Point is (-2, 0)

Option 1)

(2, 4)

This option is incorrect.

Option 2)

(–2, 0)

This option is correct.

Option 3)

(–1, 1)

This option is incorrect.

Option 4)

(0, 2)

This option is incorrect.

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