If normal at P on the curve `y^2 - 3x^2 + y + 10 = 0` passes through the point `(0, 3/2)` ,then slope of tangent at P is n. The value of |n| is equal to

A curve passes through the point (2,0) and the slope of the tangent at any point (x, y) is x^(2)-2x for all values of x then 6y_(max) is equal to

If the circel x ^(2) + y^(2) -(3p +4) x - (p -2)y + 10p=0 passes through the point (3,1) , then value of p is-

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_____.

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_____.

Let C be a curve defined by y=e^a+b x^2dot 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_____.

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

The tangent to the curve y=x^(2)+3x will pass through the point (0,-9) if it is drawn at the point

If a tangent of slope 2 of the ellipse (x^2)/(a^2) + (y^2)/1 = 1 passes through the point (-2,0) , then the value of a^2 is equal to

If a tangent of slope 2 of the ellipse (x^2)/(a^2) + (y^2)/1 = 1 passes through the point (-2,0) , then the value of a^2 is equal to

A curve passes through the point "(2,0)" and the slope of tangent at any point (x,y) on the curve is x^(2)-2x for all values of x ,then the maximum value of y is equal to _____________