Question

Length of chord of contact of $(2,5)$ with respect to $y^2=8x$ is

• A. $\frac{3\sqrt{41}}{2}$ units
• B. $\frac{2\sqrt{17}}{3}$ units
• C. $\frac{7\sqrt{3}}{5}$ units
• D. $\frac{5\sqrt{3}}{7}$ units

Answer 1

The correct option is A $\frac{3\sqrt{41}}{2}$ units

Chord of contact of $(2,5)$ with respect to $y^2=8x$ is
$y\cdot 5=4(x+2)$
$\Rightarrow 5y-4x=8\cdots \left(1\right)$
Solving equation $\left(1\right)$ with $y^2=8x$
$y^2=(5y-8)2$
$\Rightarrow y^2-10y+16=0$
$\Rightarrow (y-8)(y-2)=0$
$\therefore y_1=8,y_2=2$
Using $\left(1\right),$ we get
$x_1=8,x_2=\frac{1}{2}$
Then the end points of chord are $(8,8)$ and $(\frac{1}{2},2)$
So, length of chord of contact
$=\sqrt{{(8-\frac{1}{2})}^2+(8-2{)}^2}$
$=\frac{3\sqrt{41}}{2}$ units