The tengent at a point (a, b) to the curve `y=sinx` is parallel to the line `2y=x.` If `agt0` find b.

The tangent to the curve y=x^2-5x+5. parallel to the line 2y=4x+1, also passes through the point :

If the tangent to the curve y=x^(3)+ax+b at (1,-6) is paralle to the line x-y+5=0 , find the a and b.

Find the point on the curve 3x^2-4y^2=72 which is nearest to the line 3x+2y+1=0.

Find the equation of the tangent line to the curve y = x^(2) – 2x +7 which is (a) parallel to the line 2x – y + 9 = 0 (b) perpendicular to the line 5y – 15x = 13.

Find the equation of the tangent to the curve y= sqrt(5x-3)-2 , which is parallel to the line 4x-2y+3=0

FInd the equation of the normal to the curve 3x^2-y^2=8 which is parallel to the line x+3y=4.

Find the equation of the tangnet to the curve y=sqrt(3x-2) which is parallel to the line 4x-2y+5=0

Find the equation of the tangent to the curve y= sqrt(3x-2) which is parallel to the line 4x-2y+5=0.

The distance of the point (3, 5) from the line 2x + 3y - 14 = 0 measured parallel to the line x - 2y = 1 is :

find all the tangents to the curve y=cos(x+y),-2pilexle2pi that are parallel to the line x+2y=0