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=m x+c touches the parabola y^2=4a(x+a), then (a) c=a/m (b) c=a m+a/m 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 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 y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then (a) m_1+m_2=0 (b) 1+m_1+m_2=0 (c) m_1m_2-1=0 (d) 1+m_1m_2=0

The line y=mx+1 is a tangent to the parabola y^2 = 4x if (A) m=1 (B) m=2 (C) m=4 (D) m=3

If the line y=mx+c touches the parabola y^(2)=12(x+3) exactly for one value of m(m gt0) , then the value of (c+m)/(c-m) is equal to

In a A B C , A D is the bisector of /_B A C . If A B=6c m , A C=5c m and B D=3c m , then D C= 11. 3 c m (b) 2. 5 c m (c) 3:5c m (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 m_1+m_2=0 (b) 1+m_1+m_2=0 m_1m_2-1=0 (d) 1+m_1m_2=0

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)

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then (a) -1 1 (c) m in R (d) none of these