Find the length of tangent of parabola $y^{2} = 12 x$ at $(3, 6)$ .

6 \sqrt{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6 \sqrt{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 \sqrt{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $6 \sqrt{2}$
We know length of the tangent $y \frac{\sqrt{1 + m^{2}}}{m}$
Here $m = \frac{d y}{d x}$
Thus $2 \frac{d y}{d x} = 12 \Rightarrow \frac{d y}{d x} = 6$
So, $Length of tangent = 6 \times \frac{\sqrt{1 + 1^{2}}}{1} = 6 \sqrt{2}$

Suggest Corrections

Similar questions

Q. Find the length of sub -tangent of parabola

y^{2} = 12 x

(3, 6)

Q. Find the length of sub normal of parabola

y^{2} = 12 x

(3, 6)

Tangents are drawn from the point $(- 1, 2)$ to the parabola $y^{2} = 4 x$ . The length of the intercept made by the line $x = 2$ on these tangents is

Given the parabola $y^{2} = 4 a x,$ find the pair of tangents from the point (2, 6) where a =2.

Q. The common tangent to the parabola

y^{2} = 32 x

and

x^{2} = 108 y

intersects the coordinate axes at the points

P

and

Q

respectively . Then length of

P Q

Join BYJU'S Learning Program

Find the length of tangent of parabola y2=12x at (3,6).

The correct option is A 6√2We know length of the tangent y√1+m2mHere m=dydxThus 2dydx=12⇒dydx=6So, Length of tangent=6×√1+121=6√2

Find the length of tangent of parabola $y^{2} = 12 x$ at $(3, 6)$ .

The correct option is A $6 \sqrt{2}$
We know length of the tangent $y \frac{\sqrt{1 + m^{2}}}{m}$
Here $m = \frac{d y}{d x}$
Thus $2 \frac{d y}{d x} = 12 \Rightarrow \frac{d y}{d x} = 6$
So, $Length of tangent = 6 \times \frac{\sqrt{1 + 1^{2}}}{1} = 6 \sqrt{2}$