What is the line tangent to the graph of x=y^{2}+5

ebnspmia0jj

ebnspmia0jj

Answered question

2022-02-10

What is the line tangent to the graph of x=y2+5 at the point (5,1)?

Answer & Explanation

Pamela Webb

Pamela Webb

Beginner2022-02-11Added 10 answers

x=y2+5
Using implicit differentiation:
D(x)=D(y2+5)
1=2y*y'+0
y=12y
Since y=1 then:
y=12×1=12
The tangent is a straight line graph of the form:
y=mx+c
So at (5,1):
1=12x+c
1=5×12+c
c=152=32
So the equation of the tangent
y=12x32

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