Prove that the straight line lx+my+n=0 touches the parabols `y^2=4ax`, if `ln=am^2`.

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

Prove that the line x/l+y/m=1 touches the parabola y^2=4a(x+b) , if m^2(l+b)+al^2=0 .

The straight line x+y=sqrt2P will touch the hyperbola 4x^2-9y^2=36 if

The value of k for which the line x+y+1=0 touches the parabola y^2 = 4kx is :

Prove that the line lx+my+n=0 toches the circle (x-a)^(2)+(y-b)^(2)=r^(2) if (al+bm+n)^(2)=r^(2)(l^(2)+m^(2))

The number of values of c such that the straight line y=4x+c touches the curve (x^2)/4+(y^2)/1=1 is (a) 0 (b) 1 (c) 2 (d) infinite

Statement I The line y=mx+a/m is tangent to the parabola y^2=4ax for all values of m. Statement II A straight line y=mx+c intersects the parabola y^2=4ax one point is a tangent line.

The condition that a straight line with slope m will be normal to parabola y^(2)=4ax as well as a tangent to rectangular hyperbola x^(2)-y^(2)=a^(2) is

If the straight line ax + by = 2 ; a, b!=0 , touches the circle x^2 +y^2-2x = 3 and is normal to the circle x^2 + y^2-4y = 6 , then the values of 'a' and 'b' are ?

Prove that the straight lines represented by (y-mx)^2=a^2 (1+m^2) and (y-nx)^2=a^2(1+n^2) form rhombus.