The curve `y=a x^3+b x^2+c x+5` touches the x-axis at `P(-2,\ 0)` and cuts the y-axis at the point `Q` where its gradient is 3. Find the equation of the curve completely.

The curve y=ax^(2)+bx^(2)+cx+5 touches the x-axis at P(-2,0) and cuts the y-axis at point Q, where its gradient is 3. Now, match the following lists and then choose the correct code.

If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at (0, 0) but touches x-axis at (1, 0) , then

The curve y=ax^(3)+bx^(2)+cx is inclined at 45^(@) to x-axis at (0,0) but it touches x-axis at (1,0) , then a+b+c+10 is

The curve x = 4 - 3y - y^(2) cuts the y-axis into two points P and Q. then the area enclosed by the y-axis and the portion of the curve which lies between P and Q is

The equation of tangent to the curve y=be^(-x//a) at the point where it crosses Y-axis is

Write the equation of the tangent to the curve y=x^2-x+2 at the point where it crosses the y-axis.

The tangent at any point (x , y) of a curve makes an angle tan^(-1)(2x+3y) with x-axis. Find the equation of the curve if it passes through (1,2).

A tangent drawn to the curve y=f(x) at P(x,y) cuts the x-axis and y-axis at A and B respectively such that BP:AP=2:1 . Given that f(1)=1 . Answer the question:Equation of normal to curve at (1,1) is (A) x-4y+3=0 (B) x-3y+2=0 (C) x-2y+1=0 (D) none of these

The circle x^2+y^2−8x+4y+4=0 touches: a) x axis b) y axis c) both the axis d) neither x axis nor y axis

A normal is drawn at a point P(x , y) of a curve. It meets the x-axis and the y-axis in point A AND B , respectively, such that 1/(O A)+1/(O B) =1, where O is the origin. Find the equation of such a curve passing through (5, 4)