P is a variable points on the hyperbola `x^2/a^2-y^2/b^2=1` whose vertex is `A(a,0)` The locus of the middle points AP is

P is a veriable poin on the hyperbola x^(2) - y^(2) =16 and A (8,0) is a fixed point . Show that the locus of the middle point of the line segment bar(AP) is another rectangular hyperbola.

P (a sec phi , a tan phi) is a variable point on the hyperbola x^(2) - y^(2) = a^(2) , and A(2a,0) is a fixed point. Prove that the locus of the middle point of AP is a rectangular hyperbola.

If P is a point on the parabola y^(2)=8x and A is the point (1,0) then the locus of the mid point of the line segment AP is

If P is a point on the parabola y^(2)=8x and A is the point (1,0) then the locus of the mid point of the line segment AP is

A chord PQ of the hyperbola xy=c^(2) is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 Find the locus of the middle point of PQ .

If P is point on the parabola y ^(2) =8x and A is the point (1,0), then the locus of the mid point of the line segment AP is

If P is a point on the parabola y^(2)=8x and A is the point (1,0) then the locus of the midpoint of the line segment AP is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is