[" Q.1If "P(x_(1),y_(1))" is a point on the hypesbolo "],[x^(2)-y^(2)=a^(2)" ,then Sp."5'p=]

If P(x_(1),y_(1)) is a point on the hyperbola x^(2)-y^(2)=a^(2) , then SP.S'P= . . . .

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the vlaue of (1)/(y_(1))+(1)/(y_(2)) is

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the vlaue of (1)/(y_(1))+(1)/(y_(2)) is

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the value of (1)/(y_(1))+(1)/(y_(2)) is

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the vlaue of (1)/(y_(1))+(1)/(y_(2)) is

If y_(1) and y_(2) are the ordinates of two points P and Q on the parabola y^(2)=4 a x and y_(3) is the ordinate of the point of intersection of the tangents at P and Q then, y_(1), y_(3) and y_(2) are in

If the distance of any point P(x,y) from the point Q(x_(1),y_(1)) is given by d(P,Q)=max.{|x-x_(1)|,|y-y_(1)|} .If Q=(1,2) and d(P,Q)=3 ,then the locus of P is

Prove that if P(x,y) be any point on the line segment joining P_(1)(x_(1),y_(1)) and P_(2) (x_(2),y_(2)) then x=x_(1)+k(x_(2)-x_(1)) and y=y_(1)+k(y_(2)-y_(1)) , where bar (P_(1)P), bar (P_(1)P_(2))=k What conclusion can you draw about the position of P if k=(1)/(2) ?

Prove that if P(x,y) be any point on the line segment joining P_(1)(x_(1),y_(1)) and P_(2) (x_(2),y_(2)) then x=x_(1)+k(x_(2)-x_(1)) and y=y_(1)+k(y_(2)-y_(1)) , where bar (P_(1)P), bar (P_(1)P_(2))=k What conclusion can you draw about the position of P if 0 lt k lt 1