Number of common tangent(s) with finite & (real) slope drawn to the curves `xy=c^(2)` & `y^(2)=4ax` is `(a>0)`

Number of common tangent with finite slope to the curves xy=c^(2) and y^(2)=4ax is:

Area common to the curves y^(2)=ax and x^(2)+y^(2)=4ax is equal to

The slope of the tangent to the curve y=6+x-x^(2) at (2,4) is

Find the number of common tangents that can be drawn to the circles x^(2)+y^(2)-4x-6y-3=0 and x^(2)+y^(2)+2x+2y+1=0

Slope of the tangent to the curve y=x^(2)+3 at x=2 is

The number of direct common tangents that can be drawn to the circles x^(2)+y^(2)+4x-6y-12=0 and x^(2)+y^(2)-8x+10y+16=0 is/are

If the line,ax+by+c=0 is a normal to the curve xy=2

The number of tangents with positive slope that can be drawn from the origin to the curve y = sinx is

The number of real tangents that can be drawn from (2, 2) to the circle x^(2)+y^(2)-6x-4y+3=0 , is

The equation of common tangent to the curves y^(2)=16x and xy=-4 is