Question

Through the focus of the parabola $y^2 = 2px (p > 0) $ a line is drawn which intersects the curve at $A(x_1 , y_1 )$ and $B(x_2 , y_2 )$. The ratio $\frac{y_1y_2}{x_1x_2}$ equals

• A. 2
• B. - 1
• C. - 4
• D. some function of p

Answer 1

Answer: (C)

$y ^2 = 4ax, 4a = 2p > 0$
$x_1 = at_1^2 , y_1 = 2at_1 $
$x_2 = at _2^2, y_2 = 2at_2$
and $t_1 t_2 = - 1$
ratio $=\frac{4a^{2}t_{1}t_{2}}{a^{2 }t_{1}^{2}t_{2}^{2}} = -4$
Note: for objective take focal chord as latus rectum