Mathematics

Problem

Consider the circle

x^{2}+y^{2}=25

and the point

P(3,4)

. a. (i) Verify that

P

lies on the circle. b. (ii) Find the equation of the tangent to the circle at

P

in general form. c. (iii) Rewrite the equation obtained in part (ii) in slope–intercept form

y=mx+c

and state the values of

m

and

c

. d. (iv) Calculate the

x

-intercept and

y

-intercept of the tangent found in part (ii).