Question

Answer the following:

Find the equation of the tangent to the parabola y² = 8x which is parallel to the line 2x + 2y + 5 = 0. Find its point of contact

Answer 1

The equation of the tangent to the parabola y² = 4ax in terms of slope m is y = `"mx" + "a"/"m"` and the point of contact is `("a"/"m"^2, (2"a")/"m")`.

The equation of parabola is y² = 8x

Comparing this with y² = 4ax, we get,

∴ 4a = 8

∴ a = 2

Slope of 2x + 2y + 5 = 0 is `-2/2` = – 1

The required tangent is parallel to it

∴ its slope = m = – 1

∴ the required equation of the tangent is

y = `(-1)"x" + 2/((-1))` = – x – 2

∴ x + y + 2 = 0

The point of contact = `("a"/"m"^2, (2"a")/"m")`

= (2, – 4)