Answer:
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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