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

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then

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

Let the lines (y-2)=m_1(x-5) and (y+4)=m_2(x-3) intersect at right angles at P (where m_1a n dm_2 are parameters). If the locus of P is x^2+y^2gx+fy+7=0 , then the value of |f+g| is__________

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)

The straight lines X axis and Y axis are perpendicular to each other . Is the condition m_1m_2=-1 true ?

The straight lines represented by (y-m x)^2=a^2(1+m^2) and (y-n x)^2=a^2(1+n^2) from a (a) rectangle (b) rhombus (c) trapezium (d) none of these

If the straight lines (x-5)/(5m)=(2-y)/(5)=(1-z)/(-1)andx=(2y+1)/(4m)=(1-z)/(-3) are perpendicular to each other, find the value of m.

The line y = mx + 1 is a tangent to the curve y^(2) = 4x if the value of m is