What is the equation of the tangent to the circle x^2 + y^2 = 16 at the point (2, 2) without using calculus.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The equation of the triangle is x^2 + y^2 = 16. The circle does not pass through the given point (2, 2) as 2^2 + 2^2 = 4 + 4 = 8 not 16.

To demonstrate how the equation of a tangent to the circle at any point can be...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

The equation of the triangle is x^2 + y^2 = 16. The circle does not pass through the given point (2, 2) as 2^2 + 2^2 = 4 + 4 = 8 not 16.

To demonstrate how the equation of a tangent to the circle at any point can be found without using calculus use the fact that the radius drawn from the point to the center is perpendicular to the tangent. Taking an appropriate point on the circle (2 , `sqrt 12)` , the slope of the radius from this point is equal to: `(sqrt 12 - 0)/(2 - 0)` = `sqrt 3`

The product of the slope of this line with the slope of a line perpendicular to this line is -1.

The slope of the tangent through (2, `sqrt 12)` is `-1/sqrt 3` . This gives the equation of the tangent as `(y - sqrt 12)/(x - 2) = -1/sqrt 3`

=> `sqrt3(y - sqrt 12) = 2 - x`

=> `x + sqrt3*y - 8 = 0`

This shows how you can find the equation of a tangent to any point on a circle without using calculus.

Approved by eNotes Editorial Team