Posted by **Anonymous** on Tuesday, November 15, 2011 at 4:59pm.

two curves are orthogonal at a point of intersection of their tangents at that point cross at right angles. Show that the curves 2x^2+3y^2=5 and y^2=x^3 are orthogonal at (1,1) and (1,-1). Use parametric mode to draw the curves and to show the tangent lines

- calculus -
**Steve**, Tuesday, November 15, 2011 at 6:28pm
By inspection, the curves intersect at (1,1) and (1,-1)

ellipse: 4x + 6yy' = 0

y' = -2x/3y

at (1,1) slope = -2/3

at (1,-1) slope = 2/3

semicubical parabola: 2yy' = 3x^2

y' = 3x/2y

at (1,1) slope = 3/2

at (1,-1) slope = -3/2

The slopes at the intersections are negative reciprocals; hence the curves are orthogonal.

## Answer this Question

## Related Questions

- calculus - if the tangent of two intersecting circles, at their points of ...
- Math - Mark each of the following True or False. ___ a. All vectors in an ...
- Calculus - Orthogonal Trajectories - Find the orthogonal trajectories of the ...
- maths - determine the co-ordinate of the poin of intersection of the curves y=x*...
- calculus - Show that the curves (y= √2sinx) and (y=√2cosx) intersect...
- Calculus - show that the curves r=asin(è) and r=acos(è) intersect at right ...
- Calculus-check my answers please - dy/dx= (y^2 -1)/x 1. Give the general ...
- Math - I'm doing a bunch of practice finals and I don't know how to approach ...
- Advanced Functions - Identify the point of intersection of these two curves: P(t...
- calculus - Find the area bounded by {y=x2−4 y=4−x2 • sketch the ...