 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-v-resit/question-1/b/solution

For

u = 1

y = v

and

x = (1 - v^{2}) /2

. For

v = 1

, they give

y = u

and

x = (u^{2} - 1) /2

. Thus the requested curves are the upper halves of the parabolas

u = 1 : x = \frac{1 - y ^{2}}{2}, y \geq 0, v = 1 : x = \frac{y ^{2} - 1}{2}, y \geq 0 .

(1/2, 0)

and opens to the left; the second parabola has vertex

(- 1/2, 0)

and opens to the right. Both pass through

(0, 1)

and are reflections of one another across the

y

-axis.

 New to topics? Read the docs here!