Question

The equation of the chord of contact of the tangents drawn from the point (3,4) to the parabola $y^2=2x$ is .

• A. x-4y+3=0
• B. x-4y-3=0
• C. x+4y+3=0
• D. x+4y-3=0

Answer 1

The correct option is A x-4y+3=0

The chord of contact of tangents drawn from the point ($x_1,y_1$) to the conic ${\mathrm{Ax}}^2+\mathrm{Bxy}+{\mathrm{Cy}}^2+\mathrm{Dx}+\mathrm{Ey}+F=0$
is ${\mathrm{Axx}}_1+\frac{B}{2}({\mathrm{xy}}_1+{\mathrm{yx}}_1)+{\mathrm{Cyy}}_1+D\left(\frac{x+x_1}{2}\right)+E\left(\frac{y+y_1}{2}\right)+F=0$
For parabola $y^2=4ax$, the equation of the chord of contact from outside point
$(x_1,y_1)$ is
y$y_1$=2a(x+$x_1$)
$⟹$ 4y=(x+3) or
x-4y+3=0