Prove that the curves x = y² and xy = k cut at right angles* if 8k² = 1. Question Prove that the curves x = y² and xy = k cut at right angles* if 8k² = 1. in progress 0 Math Iris 2 weeks 2021-10-04T01:01:24+00:00 2021-10-04T01:01:24+00:00 1 Answer 0 views 0

## Answers ( )

Answer:Given curves are x = y²——-( 1 ) ,xy = k ———–( 2 )=> x = k/yx = y² => k/y = y²k = y³y = k⅓ [ put in ( 2 )x = k/yx = k/k⅓hence, the point of intersection of of curves are (k⅔ , k⅓)NOW,we know slope of tangent = dy/dx .for x = y²2y*dy/dx = 1dy/dx = 1/2y——-( 3 )and slope of tangent at (k⅔ , k⅓) isfor xy = kx*dy/dx + y = 0dy/dx = -y/xthe slope of tangent at (k⅔ , k⅓) iswe know if two lines are perpendicular then product of there slope = -1now,(slope of tangent at curve x = y²) × (slope of tangent at curve xy = k) = -1on cubing both sides, we get,