What will be the area of triangle formed by tangents drawn from point $(2, 6)$ to the parabola $y^{2} = 16 x$ and their chord of contact?

Open in App

Solution

We know that the area of triangle formed by tangents drawn from point $(x_{1}, y_{1})$ to the parabola $y^{2} = 4 a x$ and their chord of contact is $\frac{(y_{1}^{2} - 4 a x_{1})^{\frac{3}{2}}}{2 a} .$
According to question $x_{1} = 2, y_{1} = 6$ and $a = 4.$
Putting all the values in formula we get,
Area of triangle $= \frac{((6)^{2} - 16 \times 2)^{\frac{3}{2}}}{8}$
$\Rightarrow$ Area of triangle $= \frac{(36 - 32)^{\frac{3}{2}}}{8}$
$\Rightarrow$ Area of triangle $= \frac{8}{8} = 1$ sq.unit.
Hence, the area of triangle is $1.$

Suggest Corrections

Similar questions

(h, k)

x^{2} + y^{2} = a^{2}

x^{2} + y^{2} = 25

A

x^{2} + y^{2} = \frac{a^{2}}{2}

y^{2} = 4 a x .

x

y^{2} = 4 x

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = (a > b > 0) .

a

p (6, 8)

x^{2} + y^{2} = r^{2}

x^{2} + y^{2} = r^{2}

r = . . . .

Join BYJU'S Learning Program