How to find the equation for a tangent line with a given y intercept. An equation for a circle, y^2+x^2=39592 and I have the y intercept for a tangent line y=mx+3965.

Noe Cowan

Noe Cowan

Answered question

2022-11-10

How to find the equation for a tangent line with a given y intercept.
An equation for a circle, y 2 + x 2 = 3959 2 and I have the y intercept for a tangent line y = m x + 3965.

Answer & Explanation

artirw9f

artirw9f

Beginner2022-11-11Added 20 answers

Finding the distance between 0 , 3965 and the tangent point, by using Pythagorean theorem,
3965 2 = 3959 2 + b 2
The distance,
2 ( 11886 )
This the solution of the distance formula,
( ( 0 x ) 2 + ( 3965 f ( x ) ) ) 1 2 = 2 ( 11886 )
Found that the point at which it is tangent is at,
x = 7918 1 1886 3968
Plugged this value into the derivative of the equation for the circle,
x 15673681 x 2
And the solution for the slope of the tangent line is,
2 ( 11886 3959
Annie French

Annie French

Beginner2022-11-12Added 4 answers

Consider the system
y 2 + x 2 = 3959 2
y = m x + 3965
substitute y in the equation of the circle and, for the quadratic equation obtained, impose that the discriminant is equal to 0, that is the tangency condition.

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