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 y+b=m_1(x+a) and y+b=m_2(x+a) are two tangents to the paraabola y^2=4ax 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_1 and m_2 are parameters). If the locus of P is x^2+y^2+gx+fy+7=0 , then the value of |f+g| is__________

Statement-1: y+b=m_(1) (x+a) and y+b=m_(2)(x+a) are perpendicular tangents to the parabola y^(2)=4ax . Statement-2: The locus of the point of intersection of perpendicular tangents to a parabola is its directrix.

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+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

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

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

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

A triangle has two sides y=m_1x and y=m_2x where m_1 and m_2 are the roots of the equation b alpha^2+2h alpha +a=0 . If (a,b) be the orthocenter of the triangle, then find the equation of the third side in terms of a , b and h .

STATEMENT-1: The straight lines 2x+3y+5=0and 3x-2y+1=0 are perpendicular to each other. STATEMENT-2: Two lines y=m_(1)x+c_(1)and y=m_(2)x+c_(2) where m_(1),m_(2)in R are perpendicular if m_(1),m_(2)=-1. STATEMENT-2: Two lines y=m_(1)xx+x_(1)and y=m_(2)x+c_(2)where m_(1),m_(2)inR are peprendicular if m_(1)m_(2)=-1.