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 the tangent to curve y = x^(3) – x + 1 at the point whose x-coordinate is 2.

In the curve y=x^(3)+ax and y=bx^(2)+c pass through the point (-1,0) and have a common tangent line at this point then the value of a+b+c is

The slope of the tangent to the curve y=sqrt(4-x^2) at the point where the ordinate and the abscissa are equal is -1 (b) 1 (c) 0 (d) none of these

An ellipse with major and minor axes lengths 2a and 2b , respectively, touches the coordinate axes in the first quadrant. If the foci are (x_1, y_1)a n d(x_2, y_2) , then the value of x_1x_2 and y_1y_2 is a) a^2 (b) b^2 (c) a^2b^2 (d) a^2+b^2

The equation of the circle which touches the axes of coordinates and the line x/3+y/4=1 and whose center lies in the first quadrant is x^2+y^2-2c x-2c y+c^2=0 , where c is (a) 1 (b) 2 (c) 3 (d) 6

The equation of the circle which touches the axes of coordinates and the line x/3+y/4=1 and whose center lies in the first quadrant is x^2+y^2-2c x-2c y+c^2=0 , where c is (a) 1 (b) 2 (c) 3 (d) 6

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_____.

If the line joining the points (0,3)a n d(5,-2) is a tangent to the curve y=C/(x+1) , then the value of c is 1 (b) -2 (c) 4 (d) none of these

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

If the tangent to the curve, y = x^(3) + ax -b at the point (1, -5) is perpendicular to the line, -x +y + 4 =0 , then which one of the following points lies on the curve ? (A) (-2, 2) (B) (2, -2) (C) (-2, 1) (D) (2, -1)