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 0 (b) 1 (c) 2 (d) infinite

The line y = 2x + c touches the ellipse (x^2)/(16) + (y^2)/(4) = 1 if c is equal to

The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, and 3x+2y-2=0 are concurrent is 0 (b) 1 (c) 2 (d) infinite

Show that the straight line xcosalpha+ysinalpha=p touches the curve x y=a^2, if p^2=4a^2cosalphasinalphadot

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these

The number of triangles that the four lines y = x + 3, y = 2x + 3, y = 3x + 2, and y + x = 3 form is (a) 4 (b) 2 (c) 3 (d) 1

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=3 (c) x+y=2 (d) none of these

Prove that the line y=m(x-1)+3sqrt(1+m^(2))-2 touches the circle x^(2)+y^(2)-2x+4y-4=0 for all reacl values of m.

The eccentricity of the conic represented by x^2-y^2-4x+4y+16=0 is 1 (b) sqrt(2) (c) 2 (d) 1/2

The number of tangents to the curve x^(3/2)+y^(3/2)=2a^(3/2),a >0, which are equally inclined to the axes, is 2 (b) 1 (c) 0 (d) 4

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is (a)2 (b) 0 (c) 4 (d) 1