Hello aspirant. So, as we know there are two equations that represent parabola

1. Y²=4ax

2. X²=4ay

Let the line be y=mx+c be the line. This line to become a tangent to parabola, the condition is

For case 1:

c=a/m

For case 2:

c=-am²

I am not providing the derivations here. After steps of derviations by substituting variables and equations, these are the final conditions.

Hope this helps

Regards

Nikhitha

Hi Abhi,

A line touching the parabola is said to be a tangent to the parabola provided that it satisfies certain conditions. If we have a line y = bx + c touching a parabola y ² = 4ax, then c = a/b. Similarly, the line y = bx + c touches the parabola x ² = 4ay if c =-ab ² .

I hope this information helps you.

Good Luck!