You visited us 3 times! Enjoying our articles? Unlock Full Access!

Focal Chord

Find the leng...

Question

Find the length of chord of contact of the tangents drawn from point $(x_{1}, y_{1})$ to the parabola $y^{2} = 4 a x$

Open in App

Solution

Let tangent at $P (t_{1}) & Q (t_{2})$ meet at $(x_{1}, y_{1})$
$∴ a t_{1} t_{2} = x_{1}$ & $a (t_{1} + t_{2}) = y_{1}$
$∵ P Q = \sqrt{(a t_{1}^{2} - a t_{2}^{2})^{2} + (2 a (t_{1} - t_{2}))^{2}}$
$= a \sqrt{((t_{1} + t_{2})^{2} - 4 t_{1} t_{2}) ((t_{1} + t_{2})^{2} + 4)} = \sqrt{\frac{(y {_{1}}^{2} - 4 a x_{1}) (y {_{1}}^{2} + 4 a^{2})}{a^{2}}}$

Suggest Corrections

Similar questions

(x_{1}, y_{1})

y^{2} = 4 a x

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

(x_{2}, y_{2})

(x_{1}, y_{1})

y^{2} = 4 a x

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

(x_{2}, y_{2})

y^{2} = 4 b x

y^{2} = 4 a x

A

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

y^{2} = 4 a x .

A

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

y^{2} = 4 a x

Join BYJU'S Learning Program