Find the equation of directrix of the parabola is given by 64x equals to -ySquare ​

Given equation of parabola is

and

2

=64x (i)

The point at which the tangent to the curve is parallel to the line is the nearest point on the curve.

On differentiating both sides of equation (i), we get

2 y

dx

d y

=64

⇒

dx

d y

=

and

32

Also, slope of the given line is −

3

4

∴−

3

4

=

and

32

⇒and=−24

From equation (i), (−24)

2

=64x⇒x=9

∴ the required point is (9,−24)

Explanation:

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