Question

A particle travels the circumference of the equation x^2 + y^2 = 1 counterclockwise. At what points in the circle does the ordinate(y) decrease with the same speed that the abscissa(x) grows? Use derivates

Answer 1

See below

Explanation:

For the unit circle, differentiate wrt time:

• `2 x \ dot x + 2 y \ dot y = 0`

The condition [" ordinate(y) decrease with the same speed [ sic ] that the abscissa(x) grows"] might be interpreted as:

• `dot y = - dot x`

So:

• `2 x dot x - 2 y dot x = 0`

• `dot x ( x - y ) = 0`

So that leaves solutions along:

• `y = x`.

The points on the unit circle are:

• `pm( 1/sqrt2, 1/sqrt2)`

But it's easily possible to construe the question as requiring solution along:

• `y = - x`