1. Tardigrade
  2. Question
  3. Mathematics
  4. If a line x+y=1 cut the parabola y2=4 a x in points A and B and normals drawn at A and B meet at C. The normal to the parabola from C other, than above two meet the parabola in D, then point D is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If a line $x+y=1$ cut the parabola $y^2=4 a x$ in points $A$ and $B$ and normals drawn at $A$ and $B$ meet at $C$. The normal to the parabola from $C$ other, than above two meet the parabola in $D$, then point $D$ is

Conic Sections

Solution:

image
$A\left(x_1, y_1\right), B\left(x_2, y_2\right), C\left(x_3, y_3\right)$
$y_1+y_2+y_3=0 .....$(1)
$y^2=4 a x$
$y^2=4 a(1-y)$
$y^2+4 a y-4 a=0$
$y_1+y_2=-4 a .....$(2)
Using $(2)$ in $(1)$
$y_3=4 a$
$D(4 a, 4 a)$