Question

Write the equation of the parabola whose focus is (4,0) and directrix at y = 2

Answer 1

`\left ( x-4 \right )^(2)+\left ( y-0 \right )^(2)=\left ( y-2 \right )^(2)`

Step-by-step explanation: We know that distance from a point on the parabola and focus is equal to their distance from a the directrix. Let (x, y) be the point,

So,

`\sqrt{\left ( x-4 \right )^(2)+\left ( y-0 \right )^(2)}=(\left | y-2 \right |)/(1)`

`\left ( x-4 \right )^(2)+\left ( y-0 \right )^(2)=\left ( y-2 \right )^(2)`. This is the required equation.