# Calculus

show that the curves r=asin(è) and r=acos(è) intersect at right angles.

can you show that the derivatives for each are the negative reciprocal of each other? That is the key.

i need more info..i know how to find the derivative...but how will that prove my question. Do I need to graph it after i find the derivatives?

The definition of perpendicular lines is that their slope is the negative reciprocal. The deravative is the slope.

You will need to determine the point of intersection, then evaluate the derivatives at that point. If one is the negative reciprocal of the other, then by definition, they are perpendicular.

1. 👍 0
2. 👎 0
3. 👁 209

## Similar Questions

1. ### Calculus

Show that the curves r=acos(è) and r=cos(è) intersect at right angles. can it be shown that the derivative of one is the negative reciprocal of the derivative of the other?

asked by Amy on April 5, 2007
2. ### calculus

Show that the curves (y= √2sinx) and (y=√2cosx) intersect at right angles at a certain point with 0

3. ### calculus

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

asked by Anonymous on November 15, 2011

dy/dx= (y^2 -1)/x 1. Give the general equation of the curves that satisfy this equation. 2. Show that the straight lines y=1 and y=-1 are also solutions 3. Do any of the curves you found in 1) intersect y=1? My Ans: 1. The general

asked by Hebe on November 7, 2006
5. ### calculus

Find all values of 'a' such that y=a/(x−9) and y=x^2−18x+81 intersect at right angles. show steps please :)

asked by anna on October 28, 2011
6. ### Calculus

dy/dx= (y^2 -1)/x 1. Give the general equation of the curves that satisfy this equation. 2. Show that the straight lines y=1 and y=-1 are also solutions. 3. Do any of the curves you found in 1) intersect y=1? i started by dy/(y^2

asked by Hebe on November 4, 2006
7. ### Trigonometry

Prove that sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cosA

asked by Kewal on December 30, 2011
8. ### Trigonometry

Prove that sin(n+1)Asin(n-1)A + cos(n+1)Acos(n-1)A = cos2A

asked by Kewal on December 30, 2011
9. ### engineering maths

Show that the following curves are intersect eachother orthoganally.r-(1+coso) r-(1-coso)

asked by k on August 31, 2014
10. ### Calculus Help

Let c and dd be positive real numbers. Show that regardless of c,d, the parabolas r=c/(1+cos(theta)) and r=d/{(1-costheta) intersect at rights angles

asked by Sarah on December 3, 2010

More Similar Questions