If `m` is the slope of a tangent to the curve `e^y=1+x^2,` then `|m|>1` (b) `m >1` `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 m is the slope of a tangent to the hyperbola (x^(2))/(a^(2)-b^(2))-(y^(2))/(a^(3)-b^(3)) =1 where a gt b gt 1 when

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____.

If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the angle between the lines x y=0 , then m is (a) 1 (b) 2 (c) -1/2 (d) -1

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

Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0 is of the form y=m(x-1)+3sqrt(1+m^2)-2.

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then

Consider the hyperbola H : x^2-y^2=1 and a circle S with center N(x_2,0) . Suppose that Ha n dS touch each other at a point P(x_1, y_1) with x_1>1 and y_1> 0. The common tangent to Ha n dS at P intersects the x-axis at point Mdot If (l ,m) is the centroid of the triangle P M N , then the correct expression(s) is (are) (d l)/(dx_1)=1-1/(3x1 2)forx_1>1 (d m)/(dx_1)=(x_1)/(3sqrt(x1 2-1)) for x_1> (d l)/(dx_1)=1+1/(3x1 2) for x_1>1 (d m)/(dy_1)=1/3 for x_1>0

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

The values of 'm' for which a line with slope m is common tangent to the hyperbola x^2/a^2-y^2/b^2=1 and parabola y^2 = 4ax can lie in interval: