Consider the circle of radius 5 centered at

Marzadri9lyy

Marzadri9lyy

Answered question

2022-03-25

Consider the circle of radius 5 centered at (0,0), how do you find an equation of the line tangent to the circle at the point (3,4)?

Answer & Explanation

Jaslyn Allison

Jaslyn Allison

Beginner2022-03-26Added 13 answers

Using calculus:
the equation of the circle is x2+y2=25
At the point (3,4), we are on the upper semicircle, whose equation is:
y=25x2
So dydx=1225x2(2x)=x25x2
At (3,4), we get dydx=34
So the slope of the line is 34 and the line contains the point (3,4).
y=34x+254

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