Mathematics

Problem

From the external point

A(2,3)

, tangents are drawn to the curve

y = x^2

. Let the points of contact be

P

and

Q

. a. (i) Show that the

x

-coordinates of

P

and

Q

satisfy a quadratic equation and write this equation explicitly. b. (ii) Find the coordinates of

P

and

Q

. c. (iii) Determine the equations of the tangents

AP

and

AQ

. d. (iv) Write the equations of the normals to the curve at

P

and

Q