If the tangent at any point `(4m^2,8m^3)` of `x^3-y^2=0` is a normal to the curve `x^3-y^2=0` , then find the value of `mdot`

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.

If 4x+y+k=0 is a tangent to the ellipse x^(2)+3y^(2)=3 then k = ?

If the inequality (m x^2+3x+4)//(x^2+2x+2)<5 is satisfied for all x in R , then find the value of mdot

If the angle between the two lines represented by 2x^2+5x y+3y^2+6x+7y+4=0 is tan^(-1)(m), then find the value of mdot

If he roots of the equation 12 x^2-m x+5=0 are in the ratio 2:3 then find the value of mdot

Find the asymptotes of the curve x y-3y-2x=0 .

If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two distinct points, then find the values of mdot

The slope of the normal to the curve y = 2x^(2) + 3 sin x at x = 0 is