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Question

Consider the parabola $x = - 2 y^{2}$ .

Graph of a parabola with normal lines drawn from point (c,0), showing angles and slopes for analysis.

From the point $open paren c comma 0 close paren$ , it is possible to draw three normal lines to the curve. One of these normal lines is the $x$ -axis. Determine the value of $c$ so that the other two normal lines are perpendicular to each other.

Accepted Answer

$- \frac{3}{8}$

Answer

$- \frac{3}{8}$

Answer

$- \frac{3}{8}$

Answer

$- \frac{3}{8}$

Consider the parabola x=−2y2x=-2y^2.From the point (c,0)\left(c,0\right), it is possible to draw three normal lines to the curve. One of these normal lines is the xx-axis. Determine the value of cc so that the other two normal lines are perpendicular to each other.

Consider the parabola $x = - 2 y^{2}$ .

From the point $open paren c comma 0 close paren$ , it is possible to draw three normal lines to the curve. One of these normal lines is the $x$ -axis. Determine the value of $c$ so that the other two normal lines are perpendicular to each other.