Coordinate Geometry
Hyperbola Normal
MMTS_Full_Test_13
Grade 12

Question:

The number of normals drawn from the point $(8,0)$ to the parabola $x^2=4y$ is
3
2
1
0

Step-by-Step Solution

Key Concept: Normal to $x^2=4y$ at $(2t,t^2)$: $x+ty=2t+t^3$; passes through $(8,0)$
$t^3+2t-8=0$. $t=2$: $8+4-8=4\ne0$. $t=1$: $1+2-8=-5\ne0$. Hmm, try $t=\sqrt[3]{...}$. Monotone function: only 1 real root. 1 normal.
Correct Answer: 2

Master Coordinate Geometry with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free