Q19 of 292 Page 564

Prove the tangent to the curve at the point (2, 0) and (3, 0) are at right angles.

We know that if the slope of two tangent of a curve are satisfies a relation m₁m₂ = -1, then tangents are at right angles

m₁ at (2, 0) = -1

m₂ at (3, 0) = 1

m₁m₂ = (-1)(1) = -1

So, we can say that tangent at (2, 0) and (3, 0) are at right angles.

At what point on the curve , is the tangent parallel to the y-axis?

Find the point on the curve where the tangent is parallel to the x-axis.

Find the point on the curve at which the tangent passes through the origin.

Find the point on the curve at which the equation of tangent is .