Find all points on the curve x^2y^2+xy=2 where the slope of the tangent line is -1.

Sergio Heath

Sergio Heath

Answered question

2023-02-24

Find all points on the curve x 2 y 2 + x y = 2 where the slope of the tangent line is -1.

Answer & Explanation

a4dlity3v

a4dlity3v

Beginner2023-02-25Added 6 answers

Angle OBA = 90 degrees
(By theorem, the radius across the point of contact is perpendicular to the tangent at any point on a circle.)
Pythagoras theorem in right angled ABO
O B 2 = O A 2 A B 2 r 2 = ( r + 7.5 ) 2 15 2 r 2 = r 2 + 56.25 + 15 r 225 15 r = 168.75 r = 11.25 c m D i a m e t e r = 2 r = 2 × 11.25 = 22.5 c m

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