If `y=m x+c` touches the parabola `y^2=4a(x+a),` then (a)`c=a/m` (b) `c=a m+a/m` (c)`c=a+a/m` (d) none of these

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then (a) m_1+m_2=0 (b) m_1.m_2=-1 (c) m_1+m_2=1 (d) none of these

The locus of the midpoint of the segment joining the focus to a moving point on the parabola y^2=4a x is another parabola with directrix (a) y=0 (b) x=-a (c) x=0 (d) none of these

The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c and the x-axis lie on the surface: (a.) c z=m x y (b.) x y=c m z (c.) c y=m x z (d.) none of these

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then the locus of Pdot is a) a cicle b) a parabola c) a straight line d) none of these

Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Statement 2: The line y=m x+a m+a/m touches y^2=4a(x+a) for all real values of mdot (a) Both the statements are true, and Statement-1 is the correct explanation of Statement 2. (b)Both the statements are true, and Statement-1 is not the correct explanation of Statement 2. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+c)=0 , then

lim_(x->0) (sinx^n)/((sinx)^m),(mltn), is equal to (a) 1 (b) 0 (c) n//m (d) none of these

The center of a rectangular hyperbola lies on the line y=2xdot If one of the asymptotes is x+y+c=0 , then the other asymptote is: (a) 6x+3y-4c=0 (b) 3x+6y-5c=0 (c) 3x-6y-c=0 (d) none of these

Normal drawn to y^2=4a x at the points where it is intersected by the line y=m x+c intersect at P . The foot of the another normal drawn to the parabola from the point P is (a) (a/(m^2),-(2a)/m) (b) ((9a)/m ,-(6a)/m) (c) (a m^2,-2a m) (d) ((4a)/(m^2),-(4a)/m)