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`

The triangle formed by the normal to the curve f(x)=x^2-ax+2a at the point (2,4) and the coordinate axes lies in second quadrant, if its area is 2 sq units, then a can be

The area of the triangle formed by the tangent at the point (a, b) to the circle x^(2)+y^(2)=r^(2) and the coordinate axes, is

If x lies in the interval [0,\ 1] , then the least value of x^2+x+1 is (a) 3 (b) 3//4 (c) 1 (d) none of these

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 area of triangle formed by tangent at (1,1) on y=x^(2) +bx +c with coordinate axis is equal to 1 then the integral value of b is

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 9a) a^2 (b) b^2 (c) a^2b^2 (d) a^2+b^2

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

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

The line y=mx+1 is a tangent to the curve y^2=4x if the value of m is(A) 1 (B) 2(C) 3(D) 1/2.