Let P and Q be points of the ellipse `16 x^(2) +25y^(2) = 400` so that `PQ = 96//25` and P and Q lie above major axis. Circle drawn with PQ as diameter touch major axis at positive focus, then the value of slope m of PQ is

The tangent at any point on the ellipse 16x^(2)+25y^(2) = 400 meets the tangents at the ends of the major axis at T_(1) and T_(2) . The circle on T_(1)T_(2) as diameter passes through

Let P and Q be points on the line joining A(-2, 5) and B(3, 1) such that AP = PQ = QB. If mid-point of PQ is (a, b), then the value of (b)/(a) is

From any point P lying in the first quadrant on the ellipse (x^2)/(25)+(y^2)/(16)=1,P N is drawn perpendicular to the major axis and produced at Q so that N Q equals to P S , where S is a focus. Then the locus of Q is 5y-3x-25=0 3x+5y+25=0 3x-5y-25=0 (d) none of these

Let P be a point on the ellipse x^2/a^2+y^2/b^2=1 , 0 < b < a and let the line parallel to y-axis passing through P meet the circle x^2 +y^2=a^2 at the point Q such that P and Q are on the same side of x-axis. For two positive real numbers r and s, find the locus of the point R on PQ such that PR : RQ = r : s and P varies over the ellipse.

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

P(a,5a) and Q(4a,a) are two points. Two circles are drawn through these points touching the axis of y. Centre of these circles are at

At a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 tangents PQ is drawn. If the point Q be at a distance (1)/(p) from the point P, where 'p' is distance of the tangent from the origin, then the locus of the point Q is

P and Q are any two points on the circle x^2+y^2= 4 such that PQ is a diameter. If alpha and beta are the lengths of perpendiculars from P and Q on x + y = 1 then the maximum value of alphabeta is

Let the tangent at a point P on the ellipse meet the major axis at B and the ordinate from it meet the major axis at A. If Q is a point on the AP such that AQ=AB , prove that the locus of Q is a hyperbola. Find the asymptotes of this hyperbola.