Find the gradient of the tagent to the curve `ay^(2)-bx^(2)=1` at the point (a,b)

find the equation of the tangent to the curve y=-5x^2+6x+7 at the point (1//2, 35//4)

The equation of the tangent to the curve y^(2)=ax^(3)+b at the point (2,3) on it is y=4x-5 , find a and b.

Obtain the equation of the curve passing through the point(4,3) and at any point the gradient of the tangent to the curve is the reciprocal of the ordinate of the point.

A curve is passing through the point (4,3) and at any point the gradient of the tangent to the curve is reciprocal of the ordinate of the point. Obtain the equation of the curve.

The triangle formed by the tangent to the curve f(x)=x^2+bx-b at the point (1,1) and the coordinate axes, lies in the first quadrant. If its area is 2, then the value of b is (a) -1 (b) 3 (c) -3 (d) 1

Find the slope of tangent of the curve 3x^3+2x+y=0 at the point (1,-1)

Find the coordinates of the point on the curve y=(x)/(1+x^(2)) where the tangent to the curve has the greatest slope.

The slope of the tangent line to the curve x^(3)-x^(2)-2x+y-4=0 at some point on it is. 1. Find the coordinates of such point or points.

If the equation of the tangent to the curve y^2=a x^3+b at point (2,3) is y=4x-5 , then find the values of a and b .