`m_(1),m_(2),m_(3)` are the slope of normals `(m_(1) < m_(2) < m_(3))` drawn through the point `(9,-6)` to the parabola `y^(2)=4x` and A=`[a_(ij)]` is square matrix of order 3 such that `a_(ij)` = `{:{(1, if i!=j),(m_(i), if i=j) :}``quad` Then `|A|=......`

From the point P(h, k) three normals are drawn to the parabola x^(2) = 8y and m_(1), m_(2) and m_(3) are the slopes of three normals Find the algebraic sum of the slopes of these three normals.

From the point P(h, k) three normals are drawn to the parabola x^(2) = 8y and m_(1), m_(2) and m_(3) are the slopes of three normals If two of the three normals are at right angles then the locus of point P is a conic, find the latus rectum of conic.

In triangle ABC m_(1),m_(2),m_(3) are the lenghts of the medians through A,B and C respectively . If C=(pi)/(2) , then (m_(1)^(2)+m_(2)^(2))/(m_(3)^(2)) =

Through the vertex A of the parabola ((z-bar(z))/(2i))^(2)=2(z+bar(z)), where z=x+i y , (i=sqrt(-1)) two chords AP and AQ are drawn and the circles on AP and AQ as diameters intersect in R . If m_(1) , m_(2), m_(3) are slopes of tangent to parabola at P ,tangent to parabola at Q , AR respectively then find |(1)/(m_(1)m_(3))+(1)/(m_(2)m_(3))|

If m_(1),m_(2) are the slopes of tangents to the ellipse S=0 drawn from (x_(1),y_(1)) then m_(1)+m_(2)

If m_(1),m_(2) are the slopes of two lines and theta is the angle between two lines then tan theta =

If 'm_(1)',m_(2)' are the slopes of two lines and theta is the angle between two lines then tan theta=

If m_(1) , m_(2) are the slopes of two lines and theta is the angle between two lines then tan theta =

If m_(1) and m_(2) are the slopes of tangents to x^(2)+y^(2)=4 from the point (3,2), then m_(1)-m_(2) is equal to

If m_(1)&m_(2) are the slopes of the tangents to the hyperbola (x^(2))/(25)-(y^(2))/(16)=1 which passes through the point (4,2), find the value of (i)m_(1)+m_(2)&(ii)m_(2)m_(2)