Consider the sideways parabola x = y^2 + 1. Determine the value(s) of m such that the line y + mx intersects this parabola only once.

Question

Consider the sideways parabola x = y² + 1. Determine the value(s) of m such that the line y = mx intersects this parabola only once.

 

Can you please include the process to solve this problem?

Answer 1

This sideways parabola has an axis of symmetry of y=0 with an x-intercept of (1, 0).  The only value of m where the line intersects this parabola is

 

m=0