Let `C` be a curve defined by `y=e^(a+b x^2)dot` The curve `C` passes through the point `P(1,1)` and the slope of the tangent at `P` is `(-2)dot` Then the value of `2a-3b` is_____.

The curve 3y^2=2ax^2+6b passes through the point P(3.-1) and the gradient of curve at P is -1. Find the values of a and b

If a curve passes through the point (1, -2) and has slope of the tangent at any point (x,y) on it as (x^2-2y)/x , then the curve also passes through the point

A curve passes through the point (3,-4) and the slope of the tangent to the curve at any point (x,y) is (-(x)/(y)) . Find the equation of the curve.

The slope of a curve at ( x,y) is 2x+1 . If the curve passes through the point (-4,2) , find the equation of the curve .

Find the slope of the tangent to the curve y = x^(3) – x at x = 2.

The slope of a curve at (x,y) is (x^(2)-2) and it passes through the point (3,8) . Find the equation of the curve

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

Find the equation of a curve passing through the point (-2,3), given that the slope of the tangent to the curve at any point (x,y) is (2x)/(y^(2)) .

A function y=f(x) has a second-order derivative f''(x)=6(x-1)dot It its graph passes through the point (2,1) and at that point tangent to the graph is y=3x-5, then the value of f(0) is 1 (b) -1 (c) 2 (d) 0

A curve is defined parametrically by the the equation x=t^(2) and y=t^(3). A variable pair of peerpendicular lines through the origin O meet the curve at P and Q. If the locus of the point of intersectin of the tangents at P and Q is ay^(2)=bx-1, then the value of (a+b) is "______."