The curves `y=x^3-3x^2-8x-4,y=3x^2+7x+4` touch at the point (-1, 0). The equation of the common tangent is

Prove that the curves y=x^(3)-3x^(2)-8x-4,y=3x^(2)+7x+4 touch each other and equation of the common tangent is x-y+1=0 .

The curves y=x^2-1,y=8x-x^2-9 touch each other at the point (2, 3). The equation of the common normal is

The circle x^2+y^2-8x=0 and hyperbola x^2/9-y^2/4=1 I intersect at the points A and B. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is (A) 2x-sqrt5y-20=0 (B) 2x-sqrt5y+4=0 (C) 3x-4y+8=0 (D) 4x-3y+4=0

The circles x^2+y^2-2x-4y+1=0 and x^2+y^2+4x+4y-1=0 ............a)touch internally b)touch externally c)have 3x+4y-1=0 as the common tangent at the point of contact d)have 3x+4y+1=0 as the common tangent at the point of contact

The equation of the common tangent to y^(2)=8x and x^(2)+y^(2)-12x+4=0 is

The circles x^2+y^2-2x-4y+1=0 and x^2+y^2+4x+4y-1=0 (a)touch internally (b)touch externally (c)have 3x+4y-1=0 as the common tangent at the point of contact have 3x+4y+1=0 (d)as the common tangent at the point of contact

The circles x^(2)+y^(2)-2x-4y+1=0 and x^(2)+y^(2)+4x+4y-1=0 touch internally touch externally have 3x+4y-1=0 as the common tangent at the point of contact have 3x+4y+1=0 as the common tangent at the point of contact

The circles x^2+y^2-2x-4y+1=0 and x^2+y^2+4x+4y-1=0 (a)touch internally (b)touch externally (c)have 3x+4y-1=0 as the common tangent at the point of contact (d)have 3x+4y+1=0 as the common tangent at the point of contact

or the curve y=3x^2 + 4x , find the slope of the tangent to the curve at a point where x-coordinate is -2

Find the points on the curve y=4x^3-3x+5 at which the equation of the tangent is parallel to the X-axis.