Question

Find the equation of chord of parabola
$y^2=4x$ whose midpoint is (4, 2)

• A. $x-y+2=0$
• B. $x+y+2=0$
• C. $2x+y-4=0$
• D. $x-y-2=0$

Answer 1

The correct option is D

$x-y-2=0$

Equation of the chord of the parabola $y^2=4ax$ whose middle point is $(x_1,y_1)$ is

$T=S_1$

$y{y}_1-2a(x+x_1)=y_1^2-4a{x}_1$

$y{y}_1-y_1^2=2ax+2a{x}_1-4a{x}_1$

$y_1(y-y_1)=2a(x-x_1)$

$y-y_1=\frac{2a}{y_1}(x-x_1)$

substituting ,$x_1=4,y_1=2\text{and}a=1$

$y-2=\frac{2}{2}(x-4)$

$y-2=x-4$

$x-y-2=0$