Given the endpoints (11, 23) and (6, 13) of a

indimiamimactjcf

indimiamimactjcf

Answered question

2022-04-07

Given the endpoints (11, 23) and (6, 13) of a circle, find the equation of the circle and the equation of a line tangent to the circle.

Answer & Explanation

Calvin Oneill

Calvin Oneill

Beginner2022-04-08Added 20 answers

Step 1
Finding the horizontal and vertical tangent lines is trivial. To find any tangent line on the circle, take the derivative of the parametric equations: and divide them to find the slope of a tangent line:
y y 1 = m ( x x 1 )
d d θ x = s i n ( θ )
d d θ y = c o s ( θ )
m = c o s ( θ ) s i n ( θ )
here θ can be any angle. To find x 1 and y 1 , use the same angle θ and plug it into x = 5 5 2 c o s ( θ ) + 17 / 2 and y = 5 5 2 s i n ( θ ) + 17 / 2 .
ga2t1a2dan1oj

ga2t1a2dan1oj

Beginner2022-04-09Added 1 answers

Step 1
Using vadim's idea: You know that the center is at ( 17 / 2 , 18 ) , and the radius is 5 5 / 2 . So, the point ( 17 / 2 , 18 + 5 5 / 2 ) is at the "top" of the circle. The tangent at this point is horizontal; it is the line y = 18 + 5 5 / 2 .

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Elementary geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?