Coordinate Geometry
Parabola
MMTS_Full_Test_12
Grade 12
Question:
The co-ordinate of the focus of the parabola described parametrically by $x=5t^2+2$, $y=10t+4$ is
$(3,4)$
$(7,4)$
$(4,2)$
$(2,9)$
Step-by-Step Solution
Key Concept: Convert parametric to standard form $(y-k)^2=4a(x-h)$
$y-4=10t\Rightarrow t=\frac{y-4}{10}$. $x=5t^2+2\Rightarrow (y-4)^2=20(x-2)$. Focus at $(2+5,4)=(7,4)$.
Correct Answer: 2