Question

The point \( P \) with \( x \)-coordinate \( \frac{1}{2} \) lies on the curve with equation \( y=2 x^{2} \). The normal to the curve at \( P \) intersects the curve at points \( P \) and \( Q \). Find the coordinates of \( Q \). 62

          The point \( P \) with \( x \)-coordinate \( \frac{1}{2} \) lies on the curve with equation \( y=2 x^{2} \). The normal to the curve at \( P \) intersects the curve at points \( P \) and \( Q \). Find the coordinates of \( Q \).
62

The point P with x-coordinate (1)/(2) lies on the curve with equation y=2 x^2. The normal to the curve at P intersects the curve at points P and Q. Find the coordinates of Q.
62

Added by Benjamin T.

Calculus: A Complete Course

Robert Adams , Christopher Essex 9th Edition

Chapter 0

Instant Answer

Solved by Expert Carson Merrill

11/21/2021

Step 1

Given \( x = \frac{1}{2} \) and the curve equation \( y = 2x^2 \): \[ y = 2 \left( \frac{1}{2} \right)^2 = 2 \left( \frac{1}{4} \right) = \frac{1}{2} \] So, the coordinates of \( P \) are \( \left( \frac{1}{2}, \frac{1}{2} \right) \). Show more…

Show all steps

Thanks for your feedback!

The point \( P \) with \( x \)-coordinate \( \frac{1}{2} \) lies on the curve with equation \( y=2 x^{2} \). The normal to the curve at \( P \) intersects the curve at points \( P \) and \( Q \). Find the coordinates of \( Q \). 62