If `m` is the slope of a tangent to the curve `e^y=1+x^2,` then (a)`|m|>1` (b) `m >1` (c)`m >=-1` (d) `|m|lt=1`

The line y = mx + 1 is a tangent to the curve y^(2) = 4x if the value of m is

If the slopes of the tangents and normal to the curve y=f(x) at the point (x,y) be (dy)/(dx) and m respecrtively, then the value of m is -

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then (a) m_1+m_2=0 (b) m_1.m_2=-1 (c) m_1+m_2=1 (d) none of these

If m is the slop of the normal to the continous curve y=f(x) at the point (x_(1),y_(1)) , then m is equal to-

Normals are drawn from a point P with slopes m_1,m_2 and m_3 are drawn from the point p not from the parabola y^2=4x . For m_1m_2=alpha , if the locus of the point P is a part of the parabola itself, then the value of alpha is (a) 1 (b)-2 (c) 2 (d) -1

If the slope of line through the origin which is tangent to the curve y=x^3+x+16 is m , then the value of m-4 is____.

A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is (a) ( b ) (c) y=( d ) e^(( e ) (f) K(( g ) (h) x-1( i ))( j ))( k ) (l) (m) (b) ( n ) (o) y=( p ) e^(( q ) (r) K e (s))( t ) (u) (v) (c) ( d ) (e) y=( f ) e^(( g ) (h) K(( i ) (j) x-2( k ))( l ))( m ) (n) (o) (d) None of these

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+c)=0 , then

If the tangent to the curve y^(2) = x^(3) at the point (m^(2), m^(3)) is also the normal to the curve at (M^(2), M^(3)) , then the value of mM is-

The real value of a for which the value of m satisfying the equation (a^2-1)m^2-(2a-3)m+a=0 given the slope of a line parallel to the y-axis is(a) 3/2 (b) 0 (c) 1 (d) +-1