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

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

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

Two straight lines (y-b)=m_1(x+a) and (y-b)=m_2(x+a) are the tangents of y^2=4a xdot Prove m_1m_2=-1.

If m is the slope of a tangent to the curve e^y=1+x^2, then (a) |m|>1 (b) m >1 (c) m >=-1 (d) |m|lt=1

If the straight line y=my+1 be the tangent of the parabola y^2=4x at the point (1,2), then the value of m will be

If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y_2+x y_1 is (where y_r represents the r t h derivative of y w.r.t. xdot (a) m^2y (b) m y^2 (c) m^2y^2 (d) none of these

The lines y=m_1x ,y=m_2xa n dy=m_3x make equal intercepts on the line x+y=1. Then (a) 2(1+m_1)(1+m_3)=(1+m_2)(2+m_1+m_3) (b) (1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3) (c) (1+m_1)(1+m_2)=(1+m_3)(2+m_1+m_3) (d) 2(1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3)

Let A D be a median of the A B Cdot If A Ea n dA F are medians of the triangle A B Da n dA D C , respectively, and A D=m_1,A E=m_2,A F=m_3, then (a^2)/8 is equal to (a) m_2^2+m_3^2-2m_1^2 (b) m_1^2+m_2^2-2m_3^2 (c) m_1^2+m_3^2-2m_2^2 (d) none of these

If ( m_r , 1/m_r ) where r=1,2,3,4, are four pairs of values of x and y that satisfy the equation x^2+y^2+2gx+2fy+c=0 , then the value of m_1. m_2. m_3. m_4 is a. 0 b. 1 c. -1 d. none of these

If the transversal y = m_(r)x: r = 1,2,3 cut off equal intercepts on the transversal x +y = 1 then 1 +m_(1),1 +m_(2),1+m_(3) are in