The curve with the property that the projection of the ordinate on the normal is constant and has a length equal to `a` is (a) `( b ) (c) a1n(( d ) (e)sqrt(( f ) (g) (h) y^(( i )2( j ))( k )-( l ) a^(( m )2( n ))( o ) (p))( q )+y (r))=x+c (s)` (t) (u) `( v ) (w) x+sqrt(( x ) (y) (z) a^(( a a )2( b b ))( c c )-( d d ) y^(( e e )2( f f ))( g g ) (hh))( i i )=c (jj)` (kk) (ll) `( m m ) (nn) (oo) (pp)(( q q ) (rr) y-a (ss))^(( t t )2( u u ))( v v )=c x (ww)` (xx) (yy) `( z z ) (aaa) a y=( b b b ) (ccc)tan^(( d d d ) (eee)-1( f f f ))( g g g )(( h h h ) (iii) x+c (jjj))( k k k )` (lll)

Options

A. `a" ln "(sqrt(y^(2)-a^(2)))=x+c`
B. `x+sqrt(a^(2)-y^(2))=c`
C. `(y-a)^(2)=cx`
D. `ay=tan^(-1)(x+c)`

Answer

A

Explanation

Ordinate =PM. Let `P-=(x,y)`
Projection of ordinate on normal =PN
`therefore PN=Pmcostheta=a` (Given)
`therefore y/sqrt(1+tan^(2)theta)=a`
or `y=asqrt(1+(y_(1))^(2))`
or `(dy)/(dx) = (sqrt(y^(2)-a^(2)))/(a)`
or `int(ady)/sqrt(y^(2)-a^(2))=intdx`
or `a" ln"|y+sqrt(y^(2)-a^(2))|=x+c`