Question

form differential equation representing family of lines making equal intercept on the co ordinate axis

Answer 1

My Approach :

a straight line is defined by y=mx+cy=mx+c, xx-intercept =−c/m=−c/m but −c/m=m−c/m=m, so c=−m2c=−m2.y=mx−m2,dy/dx=m,y′=my=mx−m2,dy/dx=m,y′=mStraight lines at a fixed distance pp from the origin :xcosA+ysinA=p,xcos⁡A+ysin⁡A=p,ysinA=p−xcosA,ysin⁡A=p−xcos⁡A,y=psinA−xcotA,y=psin⁡A−xcot⁡A,y′=−cotA.y′=−cot⁡A.

Are my answers correct?