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  • The length of chord of contact of the tangents drawn from the point (2,5) to the parabola <img alt="\mathrm{y^2=8 x}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7By%5E2%3D8

The length of chord of contact of the tangents drawn from the point (2,5) to the parabola \mathrm{y^2=8 x}, is

Option: 1

\frac{1}{2} \sqrt{41}


Option: 2

\sqrt{41}


Option: 3

\frac{3}{2} \sqrt{41}


Option: 4

2 \sqrt{41}


Answers (1)

best_answer

Equation of chord of contact of tangents drawn from a point \mathrm{\left(x_1, y_1\right)} to parabola \mathrm{y^2=4 a x \,\, is \, \, y y_1=2 a\left(x+x_1\right)}. So that \mathrm{5 y=2 \times 2(x+2) \Rightarrow 5 y=4 x+8}

Point of intersection of chord of contact with parabola \mathrm{y^2=8 x} are \mathrm{\left(\frac{1}{2}, 2\right),(8,8)}, So the length of chord is \mathrm{\frac{3}{2} \sqrt{41}}

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Gautam harsolia

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