Tangents are drawn to the ellipse `x^2+2y^2=2`, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

Find the equation of the common tangent in the first quadrant of the circle x^2+y^2=16 and the ellipse x^2/25+y^2/4=1 .Also find the length of the intercept of the tangent between the coordinates axes.

Locus of mid-point of the portionof the line x cos alpha + y sin alpha =p between the coordinate axes is-

Through a fixed point (h, k) secants are drawn to the circle x^2 +y^2 = r^2 . Then the locus of the mid-points of the secants by the circle is

A tangent is drawn at the point (3 sqrt(3) cos theta, sin theta) (0 lt theta lt (pi)/(2)) to the ellipse x^(2) + 27y^(2)=27 , then the least value of the sum of the intercepts on the coordinate axes by this tangent is attained when the value of theta is-

If from a point P , tangents PQ and PR are drawn to the ellipse (x^2)/2+y^2=1 so that the equation of Q R is x+3y=1, then find the coordinates of Pdot

Prove that the locus of the mid - point of the portion of the line segment made by the straigh line xcostheta+ysintheta=p upon the coordinate axes is p^(2)(x^(2)+y^(2))=4x^(2)y^(2) .

From an arbitrary point P on the circle x^2+y^2=9 , tangents are drawn to the circle x^2+y^2=1 , which meet x^2+y^2=9 at A and B . The locus of the point of intersection of tangents at A and B to the circle x^2+y^2=9 is (a) x^2+y^2=((27)/7)^2 (b) x^2-y^2((27)/7)^2 (c) y^2-x^2=((27)/7)^2 (d) none of these

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

A moving straight line always passes through the point (h,k) . Prove that the locus of the middle point of the portion of the straight line intercepted between the axes of coordinates is , (h)/(x)+(k)/(y)=2 .

Find the locus of the mid-point of the portion of the line x cosalpha+ysinalpha=4 intercepted between the axes of coordinates.